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1
Babichev, A. V., V. V. Reverdatto, O. P. Polyansky, I. I. Likhanov, and A. N. Semenov. "Heat generation due to friction in the shear crust zones as a factor of metamorphism and anatexis: the results of numerical simulation." Доклады Академии наук 486, no. 6 (June 28, 2019): 704–8. http://dx.doi.org/10.31857/s0869-56524866704-708.
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The heat release effect was estimated due to friction in faults under shear and thrust conditions by mathematical modeling, 3D and 2D thermomechanical numerical models were developed. The equations of solid mechanics in a coupled formulation were solved: the equations of mechanical equilibrium and the equation of heat transfer. The model of an elastic-plastic material with the Drucker-Prager and Huber-Mises yield function is used. For the 3D shear model, the heating was 100-110 °C for the value of the friction coefficient 0.3, 180-190 °C for 0.5, about 300 °C for 0.65. In models of horizontal thrust, the heating in the contact zone was 120-130 °C with a depth of shear plane of 20 km and 150-160 °C with a depth of shear plane of 30 km for a friction coefficient of 0.3. The results obtained can be considered as a lower estimate of the heating in the Yenisei collision-shear zone.
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Ferreira, Rui M. L., Mário J. Franca, João G. A. B. Leal, and António H. Cardoso. "Mathematical modelling of shallow flows: Closure models drawn from grain-scale mechanics of sediment transport and flow hydrodynamicsThis paper is one of a selection of papers in this Special Issue in honour of Professor M. Selim Yalin (1925–2007)." Canadian Journal of Civil Engineering 36, no. 10 (October 2009): 1605–21. http://dx.doi.org/10.1139/l09-033.
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Mathematical modelling of river processes is, nowadays, a key element in river engineering and planning. River modelling tools should rest on conceptual models drawn from mechanics of sediment transport, river mechanics, and river hydrodynamics. The objectives of the present work are (i) to describe conceptual models of sediment transport, deduced from grain-scale mechanics of sediment transport and turbulent flow hydrodynamics, and (ii) to present solutions to specific river morphology problems. The conceptual models described are applicable to the morphologic evolution of rivers subjected to the transport of poorly sorted sediment mixtures at low shear stresses and to geomorphic flows featuring intense sediment transport at high shear stresses. In common, these applications share the fact that sediment transport and flow resistance depend, essentially, on grain-scale phenomena. The idealized flow structures are presented and discussed. Numerical solutions for equilibrium and nonequilibrium sediment transport are presented and compared with laboratory and field data.
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Bovendeerd, Peter H. M., Wilco Kroon, and Tammo Delhaas. "Determinants of left ventricular shear strain." American Journal of Physiology-Heart and Circulatory Physiology 297, no. 3 (September 2009): H1058—H1068. http://dx.doi.org/10.1152/ajpheart.01334.2008.
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Mathematical models of cardiac mechanics can potentially be used to relate abnormal cardiac deformation, as measured noninvasively by ultrasound strain rate imaging or magnetic resonance tagging (MRT), to the underlying pathology. However, with current models, the correct prediction of wall shear strain has proven to be difficult, even for the normal healthy heart. Discrepancies between simulated and measured strains have been attributed to 1) inadequate modeling of passive tissue behavior, 2) neglecting active stress development perpendicular to the myofiber direction, or 3) neglecting crossover of myofibers in between subendocardial and subepicardial layers. In this study, we used a finite-element model of left ventricular (LV) mechanics to investigate the sensitivity of midwall circumferential-radial shear strain ( Ecr) to settings of parameters determining passive shear stiffness, cross-fiber active stress development, and transmural crossover of myofibers. Simulated time courses of midwall LV Ecrwere compared with time courses obtained in three healthy volunteers using MRT. Ecras measured in the volunteers during the cardiac cycle was characterized by an amplitude of ∼0.1. In the simulations, a realistic amplitude of the Ecrsignal could be obtained by tuning either of the three model components mentioned above. However, a realistic time course of Ecr, with virtually no change of Ecrduring isovolumic contraction and a correct base-to-apex gradient of Ecrduring ejection, could only be obtained by including transmural crossover of myofibers. Thus, accounting for this crossover seems to be essential for a realistic model of LV wall mechanics.
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Tripp, D. E., J. H. Hemann, and J. P. Gyekenyesi. "A Review of Failure Models for Ceramic Matrix Composite Laminates Under Monotonic Loads." Journal of Engineering for Gas Turbines and Power 112, no. 4 (October 1, 1990): 492–501. http://dx.doi.org/10.1115/1.2906194.
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Ceramic matrix composites offer significant potential for improving the performance of turbine engines. In order to achieve their potential, however, improvements in design methodology are needed. In the past most components using structural ceramic matrix composites were designed by “trial and error” since the emphasis on feasibility demonstration minimized the development of mathematical models. To understand the key parameters controlling response and the mechanics of failure, the development of structural failure models is required. A review of short-term failure models with potential for ceramic matrix composite laminates under monotonic loads is presented. Phenomenological, semi-empirical, shear-lag, fracture mechanics, damage mechanics, and statistical models for the fast fracture analysis of continuous fiber unidirectional ceramic matrix composites under monotonic loads are surveyed.
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Molina Herrera, Maritzabel, and Javier Alberto Ortíz Porras. "Behavior of cold-formed thin steel sections (MM) under concentrated loads." Ingeniería e Investigación 26, no. 3 (September 1, 2006): 12–25. http://dx.doi.org/10.15446/ing.investig.v26n3.14744.
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New sections are continually being developed in the cold-formed steel world to improve the performance of existing sections. M-section development provides an example of improving C-sections’ shear resistance and web crippling resistance against C-sections’ concentrated loads. C-sections’ shear nominal strength can be achieved through locating tow web intermediate stiffeners (M-sections) even though web crippling resistance cannot be increased in the same way. Such intermediate stiffeners mean that M-section stresses and deflections cannot be analysed with traditional material mechanics. Concentrated loads cause this behavior to become increased; 4 different models and 3 tests for each of them were thus developed, as well as determining M-sections’ theoretical resistance (based on 1996 AISI). The values obtained corresponded to maximum resistance load, visual identification of any possible type of failure, deflections (at middle span) and deformations (εx, εy, εxy). Mathematical models were also used for comparing the finite element method and simplified mathematical models’ test results for a detailed review of MM-section stress and deformation. These models were calibrated on the test results. After the failure mode was identified for each model, MM-section maximum resistance load was compared to nominal load (according to AISI formulation, also aiding formulating nominal strength calculation). The information obtained from tests and mathematical models was analysed to observe parameter (∆, σ y T) tendencies respecting applied load (P). Cyclic tests under pseudo-static loads were performed to study MM-sections’ hysteretic behavior.
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Solovei, Vladislav, Аnton Karvatskii, Taras Lazarev, Іgor Mikulionok, and Iryna Omelchuk. "Determination of the mechanical properties of 3d-printed polymer products by methods of structural mechanics." Proceedings of the NTUU “Igor Sikorsky KPI”. Series: Chemical engineering, ecology and resource saving, no. 2 (June 28, 2021): 16–32. http://dx.doi.org/10.20535/2617-9741.2.2021.235853.
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Mathematical models of stress-strain state (SSS) for modeling tests of polymer composite samples obtained by fused deposition modeling (FDM) in approximations of isotropic and orthotropic media are formulated. An algorithm for solving the inverse SSS problem to determine the effective mechanical properties in the orthotropic approximation of composite products printed by the FDM method has been developed. Numerical models have been developed to solve inverse SSS problems to determine the effective orthotropic mechanical properties of composite products with different degrees of reinforcement, obtained using additive technologies based on the FDM method. The grid convergence of the developed numerical models by the method of double recalculation is investigated. It is established that the used mesh of geometric models of product samples leads to errors in determining the vector of the modulus of elasticity in the range of 0–3.19%, and the vector of the shear modulus does not exceed 0.05–0.2%. Numerical experiments to determine the effective mechanical properties of samples of composite polymeric materials in the approximation of orthotropic homogeneous medium were performed. The obtained results are compared with the data of calculations by analytical dependences to determine the effective mechanical properties of composite materials. It is shown that the results of numerical studies agree satisfactorily with the corresponding data obtained from analytical dependences in the range of 0.081–5.696%. It is established that all three components of the vectors of modulus of elasticity and shear increase with the degree of reinforcement. The largest increase is observed for the components of vectors and , which is due to the reinforcement in the direction , and the difference between the values of the components of vectors and and and is due to the cross-sectional asymmetry of the strand. Dependences for operative prediction of effective orthotropic mechanical properties of composites based on PLA + KEVLAR 29 within the limits of change in the volume fraction of reinforcing fibers up to 5% are obtained. To develop new composite materials with predetermined properties, it is not necessary to perform multivariate, rather complex and cumbersome numerical experiments in solving the inverse SSS problem.
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Faddeev, Alexander O., Svetlana A. Pavlova, and Tatiana M. Nevdakh. "Mathematical Models and Evaluation Software for Stress-Strain State of the Earth’s Lithosphere." Engineering Technologies and Systems, no. 1 (March 29, 2019): 51–66. http://dx.doi.org/10.15507/2658-4123.029.201901.051-066.
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Introduction. For the purposes of this article, geodeformation processes mean processes associated with deformations arising from the movement of species and blocks of the lithosphere at various depths, including surfaces. The objective is to reconstruct geodynamic stress fields, which cause modern shifts and deformations in the Lithosphere. A mathematical model and software for estimating the stress-strain state of the Earth Lithosphere are considered. Materials and Methods.For mathematical modeling of stresses, isostatically reduced data on abnormal gravitation field were used. The methods of continuum mechanics and methods of the theory of differential equations were used to design a model for estimating the stressstrain state of the Earth Lithosphere. For processing input, intermediate and outcoming data, the Fourier transform method of spectral analysis for constructing grid functions and spectral-temporal method were used. To model for the stress-strain state of the Lithosphere globally, stress calculation was corrected on the basis of sputnik-derived velocity data at the surface of the earth crust. The data on the rates of horizontal and vertical movements at the surface of the Earth crust were processed to obtain a distribution of velocities in the uniform grid embracing longitudes and latitudes. The processing procedure was carried out on the basis of the Kraiging method. The software was developed in Borland Delphi 7.0 programming environment. Results. Based on the data on the abnormal gravitation field in isostatic reduction and information on the distribution of velocities of horizontal motions on the surface of the Earth crust, a mathematical model of the stress-strain state of the Lithosphere was constructed. With the help of the obtained mathematical model and software complex, the stress-strain state of the Lithosphere was calculated at various depth using elastic and elastic-viscous models, and maps of equipotential distribution of shear elastic-viscous deformations in the lithosphere at the depth of 10 km were constructed. Discussion and Conclusion. The presented mathematical model and software allow restoring fields of both elastic and elastic-viscous deformations that is fundamental for quantification of elastic-viscous shear stresses deep in the Earth Lithosphere.
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Theret, D. P., M. J. Levesque, M. Sato, R. M. Nerem, and L. T. Wheeler. "The Application of a Homogeneous Half-Space Model in the Analysis of Endothelial Cell Micropipette Measurements." Journal of Biomechanical Engineering 110, no. 3 (August 1, 1988): 190–99. http://dx.doi.org/10.1115/1.3108430.
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Experimental studies have shown that endothelial cells which have been exposed to shear stress maintain a flattened and elongated shape after detachment. Their mechanical properties, which are studied using the micropipette experiments, are influenced by the level as well as the duration of the shear stress. In the present paper, we analyze these mechanical properties with the aid of two mathematical models suggested by the micropipette technique and by the geometry peculiar to these cells in their detached post-exposure state. The two models differ in their treatment of the contact zone between the cell and the micropipette. The main results are expressions for an effective Young’s modulus for the cells, which are used in conjunction with the micropipette data to determine an effective Young’s modulus for bovine endothelial cells, and to discuss the dependence of this modulus upon exposure to shear stress.
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Burmistrova, Olga, Elena Teterevleva, Igor Grigorev, O. Kunitskaya, Andrey Manukovskiy, Sergey Rudov, and Dmitriy Vostrikov. "BASIS OF MATHEMATICAL INTERACTION MODELS OF WHEEL PROPELLERS OF FORESTRY MACHINES WITH SLIDING SURFACES." Forestry Engineering Journal 10, no. 1 (April 6, 2020): 173–84. http://dx.doi.org/10.34220/issn.2222-7962/2020.1/22.
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The purpose of the research, the results of which are presented in this article, is to analyze the scientific description of the properties of weak bearing movement surfaces of forest machines. The analysis has showed that universal mathematical models of the wheel propeller interaction with soil are based on the provisions of soil mechanics. This approach has been tested in the science of forestry production. It is successfully used by modern domestic and foreign researchers. However, with regard to the development and implementation of a mathematical description of interaction of ultra-low pressure
wheeled mover (for example, in all-terrain wheeled vehicle) with supporting surfaces, it is necessary to take into account the ratio of the sides of the mover’s contact spot with the soil, since: mover pressure on the ground is defined as the partial load of a single mover and the area contact spots; the distribution of compressive stress over the depth of the soil mass depends on the ratio of the length and width of the contact spot; the bearing capacity characterizing the resistance to shear of the soil layers depends not only on its physical and mechanical properties, but also on the parameters of the contact spot, which is
taken into account by special correction factors, the values of which depend on the aspect ratio of the contact spot. Soil rheology is considered to take into account the number of passes of a wheeled all-terrain vehicle along the route and its speed. One of the characteristics of the impact of the mover is exposure time. Value of the length of the contact spot is also used when determining the impact time of the mover on the soil.
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Burova, Iva, Ivan Wall, and Rebecca J. Shipley. "Mathematical and computational models for bone tissue engineering in bioreactor systems." Journal of Tissue Engineering 10 (January 2019): 204173141982792. http://dx.doi.org/10.1177/2041731419827922.
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Research into cellular engineered bone grafts offers a promising solution to problems associated with the currently used auto- and allografts. Bioreactor systems can facilitate the development of functional cellular bone grafts by augmenting mass transport through media convection and shear flow-induced mechanical stimulation. Developing successful and reproducible protocols for growing bone tissue in vitro is dependent on tuning the bioreactor operating conditions to the specific cell type and graft design. This process, largely reliant on a trial-and-error approach, is challenging, time-consuming and expensive. Modelling can streamline the process by providing further insight into the effect of the bioreactor environment on the cell culture, and by identifying a beneficial range of operational settings to stimulate tissue production. Models can explore the impact of changing flow speeds, scaffold properties, and nutrient and growth factor concentrations. Aiming to act as an introductory reference for bone tissue engineers looking to direct their experimental work, this article presents a comprehensive framework of mathematical models on various aspects of bioreactor bone cultures and overviews modelling case studies from literature.
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Zaoui, Fatima Zohra, Djamel Ouinas, Belkacem Achour, Mabrouk Touahmia, Mustapha Boukendakdji, Enamur R. Latifee, Ahmed A. Alawi Al-Naghi, and Jaime Aurelio Viña Olay. "Mathematical Approach for Mechanical Behaviour Analysis of FGM Plates on Elastic Foundation." Mathematics 10, no. 24 (December 15, 2022): 4764. http://dx.doi.org/10.3390/math10244764.
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This paper presents the flexural analysis of functionally graded plates resting on elastic foundations using new two-dimensional (2D) and quasi-three-dimensional (quasi-3D) higher order shear deformation theories. The main interesting feature of this theory is that it proposes a new displacement field with undetermined integral variables which involves only five unknown functions, unlike other shear and normal deformation theories, hence making it easier to use. A parabolic transverse shear deformation shape function satisfying the zero shear stress conditions on the plate outer surfaces is considered. The elastic foundation follows the Pasternak mathematical model. The material properties change continuously across the thickness of the FG plate using different distributions: power law, exponential, and Mori–Tanaka models. The governing equations of FG plates subjected to sinusoidal and uniformly distributed loads are established through the principle of virtual works and then solved via Navier’s procedure. In this work, a detailed discussion on the influence of material composition, geometric parameters, stretching effect, and foundation parameters on the deflection, axial displacements, and stresses is given, and the obtained results are compared with those published in previous works to demonstrate the accuracy and the simplicity of the present formulations. The different obtained results were found to be in good agreement with the available solutions of other higher-order theories. The proposed model is able to represent the cross section warping in the deformed shape and to demonstrate the validity and efficiency of the approach, the findings reported herein prove that this theory is capable of predicting displacements and stresses more accurately than other theories, as its results are closer when compared to numerical methods reported in other literatures.
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Kumar, D. V. T. G. Pavan, and B. K. Raghu Prasad. "Higher-Order Beam Theories for Mode II Fracture of Unidirectional Composites." Journal of Applied Mechanics 70, no. 6 (November 1, 2003): 840–52. http://dx.doi.org/10.1115/1.1607357.
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Mathematical models, for the stress analyses of unidirectional end notch flexure and end notch cantilever specimens using classical beam theory, first, second, and third-order shear deformation beam theories, have been developed to determine the interlaminar fracture toughness of unidirectional composites in mode II. In the present study, appropriate matching conditions, in terms of generalized displacements and stress resultants, have been derived and applied at the crack tip by enforcing the displacement continuity at the crack tip in conjunction with the variational equation. Strain energy release rate has been calculated using compliance approach. The compliance and strain energy release rate obtained from present formulations have been compared with the existing experimental, analytical, and finite element results and found that results from third-order shear deformation beam theory are in close agreement with the existing experimental and finite element results.
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Guz, I. A., J. J. Rushchitsky, and A. N. Guz. "Effect of a special reinforcement on the elastic properties of micro- and nanocomposites with polymer matrix." Aeronautical Journal 117, no. 1196 (October 2013): 1019–36. http://dx.doi.org/10.1017/s0001924000008666.
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AbstractThe paper revisits some of the well-known models in the mechanics of structurally heterogeneous media for the purpose of analysing their suitability to describe properties of nanocomposites and their mechanical behaviour. It also presents a new multi-component model for predicting the mechanical properties of micro- and nanocomposites reinforced either by whiskerising the microfibres or by bristlising the nanowires. The mathematical formulation of the model is based on using the Muskhelishvili complex potentials for each domain occupied by a separate component. As an example, the effective elastic constants are computed for fibrous composites with four different densities of whiskerisation. It is shown that the increase in the number of bristles per unit surface of the fibres gives a very strong rise to the value of Young’s modulus. However, the shear modulus, being the driving parameter for the strength estimation of the entire composition, is less sensitive to this factor.
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Merdaci, S., S. Boutaleb, H. Hellal, and S. Benyoucef. "Analysis of Static Bending of Plates FGM Using Refined High Order Shear Deformation Theory." Journal of Building Materials and Structures 6, no. 1 (March 31, 2019): 32–38. http://dx.doi.org/10.34118/jbms.v6i1.66.
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This work deals with the analysis of the mechanical bending behavior of a rectangular plate simply supported on four sides (FGM), subjected to transverse static loading. The high order theory is used in this work, The developed models are variably consistent, have a strong similarity with the classical plate theory in many aspects, do not require correction to the shear factor, and give rise to variations transverse shear stresses such as transverse shear parabolically varies across the shear thickness and satisfies surface conditions without stresses. Equilibrium equations are obtained by applying the principle of virtual works. The mathematical expressions of the arrow, the stresses are obtained using Navies approach to solve the system of equilibrium equations. The influence of mechanical loading and the change of the parameter of the material on mechanical behavior of the plate P-FGM are represented by a numerical example.
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Petrushin, G. D., and A. G. Petrushina. "Determination of the area of mechanical hysteresis loop using mathematical models." Industrial laboratory. Diagnostics of materials 86, no. 5 (May 22, 2020): 59–64. http://dx.doi.org/10.26896/1028-6861-2020-86-5-59-64.
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A method of the hysteresis loop relates to the direct methods for determination of the energy dissipation and studying the inelasticity in the material. The method is based on the direct formation of the mechanical hysteresis loop by static loading and unloading of the sample and measuring of the corresponding deformations. The relative energy dissipation is defined as the ratio of the hysteresis loop area to the elastic energy corresponding to the maximum amplitude of strain. Construction of the hysteresis loop is performed on the installation «torsional pendulum for determination of the mechanical properties of materials» which can work as a device for measuring internal energy dissipation by damped oscillations, and as a precision torsion test machine using a deforming device. The aim of this work is to determine the area of the static hysteresis loop through the choice of the mathematical models of loading and unloading curves with subsequent numerical integration using the ordinate values at equidistant points. The analysis of using polynomials of the second or third degree was carried out according to the criterion of the smallest sum of squared deviations between the empirical and calculated values of the function. The experimentally obtained coordinates of the points of the deformation diagram of the sample during loading and unloading were used as initial data for estimation of regression coefficients in polynomial equations. A distinctive feature of the proposed method is that analytical dependences between stresses and strains obtained by N. N. Davidenkov and containing hard-to-determine geometric parameters of the loop, which must be pre-set from the known values of the logarithmic decrement of oscillations obtained from the experiment are not used in the developed method to calculate the area of the static hysteresis loop. It is shown that a comparative assessment of the relative energy scattering in the ferrite gray iron performed by the direct method of determining the area of the mechanical hysteresis loop at different amplitudes of shear deformation, is in good agreement with the data obtained by the indirect method of damped oscillations on an installation of the similar class.
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Guerin, Heather Anne L., and Dawn M. Elliott. "The Role of Fiber-Matrix Interactions in a Nonlinear Fiber-Reinforced Strain Energy Model of Tendon." Journal of Biomechanical Engineering 127, no. 2 (November 18, 2004): 345–50. http://dx.doi.org/10.1115/1.1865212.
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The objective of this study was to develop a nonlinear and anisotropic three-dimensional mathematical model of tendon behavior in which the structural components of fibers, matrix, and fiber-matrix interactions are explicitly incorporated and to use this model to infer the contributions of these structures to tendon mechanical behavior. We hypothesized that this model would show that: (i) tendon mechanical behavior is not solely governed by the isotropic matrix and fiber stretch, but is also influenced by fiber-matrix interactions; and (ii) shear fiber-matrix interaction terms will better describe tendon mechanical behavior than bulk fiber-matrix interaction terms. Model versions that did and did not include fiber-matrix interaction terms were applied to experimental tendon stress-strain data in longitudinal and transverse orientations, and the R2 goodness-of-fit was evaluated. This study showed that models that included fiber-matrix interaction terms improved the fit to longitudinal data (RToe2=0.88,RLin2=0.94) over models that only included isotropic matrix and fiber stretch terms (RToe2=0.36,RLin2=0.84). Shear fiber-matrix interaction terms proved to be responsible for the best fit to data and to contribute to stress-strain nonlinearity. The mathematical model of tendon behavior developed in this study showed that fiber-matrix interactions are an important contributor to tendon behavior. The more complete characterization of mechanical behavior afforded by this mathematical model can lead to an improved understanding of structure-function relationships in soft tissues and, ultimately, to the development of tissue-engineered therapies for injury or degeneration.
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Reinhardt, W. D., and R. N. Dubey. "Application of Objective Rates in Mechanical Modeling of Solids." Journal of Applied Mechanics 63, no. 3 (September 1, 1996): 692–98. http://dx.doi.org/10.1115/1.2823351.
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A unified formulation is developed for deformation-related spins, and for objective rates based on them. The approach generalizes the underlying concepts, and allows new rates to be constructed. Mathematical and thermodynamical restrictions on these are shown. As a result, it can be demonstrated that the Eulerian strain rate is an objective rate of logarithmic strain, based on a spin easily derivable from the general form. Interrelations between other known spins and objective rates emerge very clearly. Consequences of the proposed formalism are explored in hypoelastic and in rigid-plastic constitutive relations, the latter involving purely isotropic and purely kinematic hardening. The application of the resulting models to the simple shear deformation is shown.
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Bardella, Lorenzo. "Reliability of first-order shear deformation models for sandwich beams." Journal of Mechanics of Materials and Structures 3, no. 7 (September 1, 2008): 1187–206. http://dx.doi.org/10.2140/jomms.2008.3.1187.
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Paimushin, V. N., V. A. Firsov, and V. M. Shishkin. "MATHEMATICAL MODELING OF THE VIBRATIONS PROPAGATION IN THIN-WALL FRAMEWORK STRUCTURES. 2. FINITE ELEMENT MODELS AND NUMERICAL EXPERIMENTS." Problems of Strength and Plasticity 84, no. 3 (2022): 311–30. http://dx.doi.org/10.32326/1814-9146-2022-84-3-311-330.
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Based on the refined S.P. Timoshenko shear model, one-dimensional finite elements for modeling the dynamic response of flat rods with clamped section of finite length on one of the front faces have been constructed. To analyze their stationary dynamic response under harmonic external action, a system of resolving equations in a complex form is formed. Three models of kinematic conjugation of clamped and free sections of rods are developed using the equation of connection between the rotation angle of the cross section and axial displacement at the boundary between the marked parts of the rod, the transitional finite element, and the concept of a single finite element with nodes located on one of its front faces. It is noted that for practical implementation, the most convenient model is one that uses a single finite element to represent fixed and free sections of the rod. On the basis of the noted model, a finite element solution of the problem of transverse bending vibrations of a cantilevered flat rod under vibration loading conditions by a periodic axial force applied to the end section of a clamped section of finite length, as well as the problem of transverse bending vibrations of a flat rod with two free ends and clamped length section between them under vibration loading by a transverse force on one of the free ends of the rod was found. The results of the finite element solution of the noted two problems are in good agreement with the previously obtained exact analytical solutions found on the basis of the S.P. Timoshenko shear model. The presence of a significant transformation of the parameters of the stress-strain state of the considered rods during the transition through the boundary from free to the clamped length areas on one of the face surfaces is noted.
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Cloud, J. E., and P. E. Clark. "Alternatives to the Power-Law Fluid Model for Crosslinked Fluids." Society of Petroleum Engineers Journal 25, no. 06 (December 1, 1985): 935–42. http://dx.doi.org/10.2118/9332-pa.
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Summary Measuring the rheological properties of crosslinked fracturing fluids is difficult but important. Fluid properties play a key role in the determination of the final geometry of the created fracture and in the distribution of proppant within the fracture; therefore, an accurate knowledge of these parameters is necessary for optimum treatment design. The first paper1 in this series described a method to measure accurately and reproducibly the rheological properties of crosslinked fracturing fluids. The technique is the first that applies long-accepted mathematical methods to correct the measurements for the deviations in shear rate caused by the non-Newtonian nature of the fluids. This, in turn, allows the rigorous examination of mathematical fluid models to determine which, if any, best describes the flow properties of the fluids. Introduction The problems of characterizing crosslinked fracturing fluids were outlined in the first paper1 in this series. These problems made the application of accepted mathematical techniques to correct measurements for deviations caused by the non-Newtonian character of these fluids difficult to justify. As a result, not making corrections has often led to the wrong choice of fluid models when the mathematical description of the fluid flow is attempted. The technique1 that was used to gather data for this study has been described previously. Dynamic mechanical testing provides a quantity - called the complex viscosity (µ*) - that has been shown by Cox and Merz2 to equal the apparent viscosity (µa) determined in steady-shear measurements. Yasuela et al.3 recently confirmed this relationship with a wide variety of instruments. Use of this relationship, coupled with the increased sensitivity and reproducibility of the mechanical spectrometer, allows an examination of the data analysis techniques currently used in the industry. The API4 currently specifies that the data gathered on fracturing fluids be reported as n' and k', which have been derived from apparent Newtonian shear rates. This promotes consistency in the presentation of data but can lead to the misinterpretation of the results of an experiment. When necessary, model-independent shear-rate conversions were applied before analysis to all the input data in this study to avoid misinterpretation of the results. Background: Analysis of Laboratory Rheology Data The procedure for determining fluid-flow characteristics from laboratory data may be expressed generally as occurring in three distinct, but not independent, steps:data acquisition,analysis and data reduction, andscale-up with the fundamental equations of fluid mechanics or some generalized method, such as that of Metzner and Reed,5 that is based on those relationships. Only the first and second steps are discussed here; a complete discussion of the third step is beyond the scope of this study. Data Acquisition Data for scale-up are normally acquired in the laboratory with capillary-, tube- and extrusional-type rheometers or parallel-plate, cone-and-plate, and concentric-cylinder rotational-type rheometers. When crosslinked gels are measured, each measurement technique suffers from the effects of the viscoelastic nature1 of the gels. Slip at the wall in capillary- and tube-type rheometers makes data obtained with this type of measurement difficult to reproduce. Slip at the wall and the Weissenberg effect complicate the interpretation of data derived from the steady-shear mode of rotational-type viscometers. The method of dynamic testing1 avoids many of those problems and provides reproducible data for the next step in the scale-up process. Analysis and Data Reduction The first step in the data analysis process is the conversion of the experimental measurements - i.e., pressure drop and pump rate or torque and angular velocity - into estimates of shear stress and shear rate. Three methods of conversion can be used:equivalent (apparent) Newtonian shear rate or viscosity,model-dependent conversions, andmodel-independent conversions. Method 1 is specified by API as the method of reporting fluid data. The shear rate, computed as if the fluid were a Newtonian liquid, is used to estimate parameters for non-Newtonian fluid models. It can be shown that this technique is adequate for certain two-parameter models, provided that restrictions are applied to the range of scale-up shear rates and that the rheological parameters are used without modification in generalized methods of scale-up. This method is inadequate, however, if the object of the experiment is both fluid-model optimization and fluid-flow scale-up. The assumptions inherent to this technique will introduce a bias toward three-parameter models that will be carried through the scale-up process, if not isolated and minimized during error determination. Data Acquisition Data for scale-up are normally acquired in the laboratory with capillary-, tube- and extrusional-type rheometers or parallel-plate, cone-and-plate, and concentric-cylinder rotational-type rheometers. When crosslinked gels are measured, each measurement technique suffers from the effects of the viscoelastic nature1 of the gels. Slip at the wall in capillary- and tube-type rheometers makes data obtained with this type of measurement difficult to reproduce. Slip at the wall and the Weissenberg effect complicate the interpretation of data derived from the steady-shear mode of rotational-type viscometers. The method of dynamic testing1 avoids many of those problems and provides reproducible data for the next step in the scale-up process. Analysis and Data Reduction The first step in the data analysis process is the conversion of the experimental measurements - i.e., pressure drop and pump rate or torque and angular velocity - into estimates of shear stress and shear rate. Three methods of conversion can be used:equivalent (apparent) Newtonian shear rate or viscosity,model-dependent conversions, andmodel-independent conversions. Method 1 is specified by API as the method of reporting fluid data. The shear rate, computed as if the fluid were a Newtonian liquid, is used to estimate parameters for non-Newtonian fluid models. It can be shown that this technique is adequate for certain two-parameter models, provided that restrictions are applied to the range of scale-up shear rates and that the rheological parameters are used without modification in generalized methods of scale-up. This method is inadequate, however, if the object of the experiment is both fluid-model optimization and fluid-flow scale-up. The assumptions inherent to this technique will introduce a bias toward three-parameter models that will be carried through the scale-up process, if not isolated and minimized during error determination.
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Ahmad, Bilal, and Xiangfan Fang. "Modeling Shear Behavior of Woven Fabric Thermoplastic Composites for Crash Simulations." Applied Composite Materials 27, no. 6 (November 20, 2020): 739–65. http://dx.doi.org/10.1007/s10443-020-09844-0.
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AbstractWoven fabric thermoplastic composites possess high specific strength and stiffness along with thermoformability. To utilize the full potential of these materials to achieve better crash-safe designs in automotive structural parts, the measurement of non-linear shear behavior and its material modeling for FEM simulations is required. The standard testing method was used to measure the pure shear behavior of woven fabric composites. These results were compared with the shear behavior of material in the presence of normal stresses along the fiber direction. Tensile and compression cyclic testing of ± 45° laminate were carried out to measure the stiffness degradation and hardening of the material in the presence of tensile normal and compression normal stress. A methodology is proposed for taking into account the differences in shear behavior under different loading directions in an FEM simulation. Based on the experimental evidence, improvements in the mathematical description of plasticity and damage in continuum damage mechanics models are proposed. The model was implemented as a user-defined material subroutine (VUMAT) for Abaqus. The experimental results from coupon tests were used to verify the results of a single element simulation. Finally, a three-point bending test was used to validate the predictions of the user material model.
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Ter-Martirosyan, Armen, Vitalii Sidorov, and Evgeny Sobolev. "Dynamic Properties of Soil Cements for Numerical Modelling of the Foundation’s Basis Transformed under the Technology of Deep Soil Mixing: A Determination Method." Buildings 12, no. 7 (July 16, 2022): 1028. http://dx.doi.org/10.3390/buildings12071028.
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This research investigates the mechanical properties of soil-cement specimens ranging from ultrasmall to large values of shear strain at dynamic loading. The nonlinear behavior of soil cement exposed to dynamic loading in a wide range of changing shear strains was examined on the basis of two mechanical models. All soil-cement specimens were collected from under an existing building and modified with deep soil mixing (DSM.). Soil-cement samples were examined using low-amplitude oscillations in the resonant column and the dynamic triaxial compression method. Additionally, the stress–strain state for modified footings exposed to dynamic loading, and the approximation of soil stiffness and damping coefficient was analyzed. Dependencies on the basis of the resilient elastic models of Ramberg–Osgood and Hardin–Drnevich are proposed for application. Results reveal that the empirical graphs of the dependency soil stiffness–shear strain based on various methods exhibited the distinctive S-shape of decreased stiffness. The stiffness of the soil cement was reduced by 50% of the maximal value at shear strains of the 10−3 decimal order. The method presented in this study enables the drawing of stiffness change and damping–shear strain dependency where the range of shear strains changes from ultrasmall to large strains. The normalized modulus of shearing and the damping coefficient on shear strains for soil cement could be obtained under the proposed method. This method can be used for the preliminary calculations of structures on the footing modified by mathematical modelling or when field research data from site investigation are not available.
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Eshmatov, Bakhtiyor, and Subrata Mukherjee. "Nonlinear Vibrations of Viscoelastic Composite Cylindrical Panels." Journal of Vibration and Acoustics 129, no. 3 (November 4, 2006): 285–96. http://dx.doi.org/10.1115/1.2730532.
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This paper is devoted to mathematical models of problems of nonlinear vibrations of viscoelastic, orthotropic, and isotropic cylindrical panels. The models are based on Kirchhoff-Love hypothesis and Timoshenko generalized theory (including shear deformation and rotatory inertia) in a geometrically nonlinear statement. A choice of the relaxation kernel with three rheological parameters is justified. A numerical method based on the use of quadrature formulas for solving problems in viscoelastic systems with weakly singular kernels of relaxation is proposed. With the help of the Bubnov-Galerkin method in combination with a numerical method, the problems in nonlinear vibrations of viscoelastic orthotropic and isotropic cylindrical panels are solved using the Kirchhoff-Love and Timoshenko hypothesis. Comparisons of the results obtained by these theories, with and without taking elastic waves propagation into account, are presented. In all problems, the convergence of Bubnov-Galerkin’s method has been investigated. The influences of the viscoelastic and anisotropic properties of a material, on the process of vibration, are discussed in this work.
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Gavrilyuk, Sergey L., and Henri Gouin. "Variational formulation for models of shear shallow water flows and ideal turbulence." International Journal of Non-Linear Mechanics 119 (March 2020): 103312. http://dx.doi.org/10.1016/j.ijnonlinmec.2019.103312.
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Rajagopal, K. R., and Giuseppe Saccomandi. "The mechanics and mathematics of the effect of pressure on the shear modulus of elastomers." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 465, no. 2112 (September 25, 2009): 3859–74. http://dx.doi.org/10.1098/rspa.2009.0416.
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In this paper, we discuss the need for models that express the stretch (or strain) as a function of stress, or implicit constitutive models that relate the stretch (or strain) and stress, for describing the elastic response of some elastomers. We would like to provide an explanation for some experimental data for elastomeric materials that imply that the material moduli depend on pressure. Included in the class of models that are proposed are those which can explain limiting chain extensibility that is exhibited by some rubber-like solids. The models that are proposed stem from a completely different starting point from that for classical elastic bodies, so that these models cannot be obtained within the context of classical theory.
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Wang, Yunliang, Frank G. Jacobitz, and Christopher J. Rutland. "Large eddy simulation of homogeneous shear flows with several subgrid-scale models." International Journal for Numerical Methods in Fluids 50, no. 7 (2006): 863–83. http://dx.doi.org/10.1002/fld.1081.
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Tarrés, Quim, and Mònica Ardanuy. "Evolution of Interfacial Shear Strength and Mean Intrinsic Single Strength in Biobased Composites from Bio-Polyethylene and Thermo-Mechanical Pulp-Corn Stover Fibers." Polymers 12, no. 6 (June 8, 2020): 1308. http://dx.doi.org/10.3390/polym12061308.
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In this article, with the aim of promoting sustainability, contributing to the circular economy and the fight against climate change, the production of composite materials from Bio-polyethylene reinforced with corn stover fibers has been studied. The behavior of the materials obtained has been studied experimentally and by mathematical models of micromechanics. The composite materials were produced by extrusion and then injection with from 10 to 50 wt.% of fibers. The creation of a good fiber-matrix interface was studied by the incorporation of coupling agent between (0–8 wt.%). Increase of 131.2% on tensile strength for 40wt.% reinforcement was achieved by adding 6 wt.% of coupling agent. The correct interface was demonstrated by a correlation of 0.99 between the experimental results and the results of the mathematical models used.
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Jalali, Amir, Hashem Dianati, Mahmood Norouzi, Hossein Vatandoost, and Mojtaba Ghatee. "A novel bi-directional shear mode magneto-rheological elastomer vibration isolator." Journal of Intelligent Material Systems and Structures 31, no. 17 (July 21, 2020): 2002–19. http://dx.doi.org/10.1177/1045389x20942314.
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In this article, a novel bi-directional shear mode magneto-rheological elastomer–based vibration isolator has been designed, fabricated, and characterized to improve the dynamic response and identification of this class of “intellectual” mechanical devices. A heuristic embodiment has been realized in order to design such an isolator wherein both the vertical and horizontal directions can be operated only in the shear mode not only individually but also simultaneously. Two fixtures have been designed for performing the characterization of the magneto-mechanical behavior of the proposed magneto-rheological elastomer isolator in the vertical and horizontal shear modes under wide ranges of strain amplitude (4%–32%), excitation frequency (1–8 Hz), and magnetic flux density (0–220 mT). Experimental results revealed maximum relative magneto-rheological effects of 35% and 27 % in the vertical and horizontal shear modes, respectively. Furthermore, basic mathematical models of single-degree-of-freedom systems, employing the magneto-rheological elastomer–based isolator in the vertical and horizontal shear modes, have been established. The proposed magneto-rheological elastomer isolator in the vertical mode exhibited natural frequency shift of 6.1% by a small increment in the magnetic flux density which approves the potential of the proposed bi-directional shear mode magneto-rheological elastomer–based vibration isolator for vibration control applications, such as seat suspension systems.
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Xie, Shijie, Hang Lin, Yixian Wang, Yifan Chen, Wei Xiong, Yanlin Zhao, and Shigui Du. "A statistical damage constitutive model considering whole joint shear deformation." International Journal of Damage Mechanics 29, no. 6 (January 23, 2020): 988–1008. http://dx.doi.org/10.1177/1056789519900778.
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The whole shear deformation of rock joints significantly affects the long-term behavior and safety of engineering projects. In this paper, a new damage constitutive model related to the Weibull distribution and statistical damage theory is proposed. This model considers the shear stiffness degradation, post-peak softening, and residual phase of rock joints in the whole shearing process. Main works include the three following aspects: First, the phase of initial damage is determined on the assumption that the joint shear failure is regarded as a result of damage evolution, according to the typical joint shear curve and the three-parameter Weibull distribution. Then, a statistical damage evolution model for the whole joint shearing process is introduced to make this model be capable of describing the residual phase of rock joints. Finally, a statistical constitutive model for the whole joint shearing process is proposed by statistical damage theory, and the calculated results of the models are compared to the experimental results. The results indicate that the proposed model shows a good agreement with the experimental examples, and the proposed model can distinctly reflect the effects of residual stress, peak stress, and shear stiffness. In addition, the model parameters can be mathematically confirmed and have distinct physical meanings.
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Ni, Yufang, Zhixian Cao, and Qingquan Liu. "Mathematical modeling of shallow-water flows on steep slopes." Journal of Hydrology and Hydromechanics 67, no. 3 (September 1, 2019): 252–59. http://dx.doi.org/10.2478/johh-2019-0012.
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Abstract A 2D hydrodynamic (labeled as CAR) model has been proposed in a rectangular Cartesian coordinate system with two axes within the horizontal plane and one axis along the vertical direction (global coordinates), considering the effects of bed slope on both pressure distribution and bed shear stresses. The CAR model satisfactorily reproduces the analytical solutions of dam-break flow over a steep slope, while the traditional Saint-Venant Equations (labeled as SVE) significantly overestimate the flow velocity. For flood events with long duration and large mean slope, the CAR and the SVE models present distinguishable discrepancies. Therefore, the proposed CAR model is recommended for applications to real floods for its facility of extending from 1D to 2D version and ability to model shallow-water flows on steep slopes.
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Kamenskiy, Alexey V., Iraklis I. Pipinos, Yuris A. Dzenis, Prateek K. Gupta, Syed A. Jaffar Kazmi, and Jason N. MacTaggart. "A mathematical evaluation of hemodynamic parameters after carotid eversion and conventional patch angioplasty." American Journal of Physiology-Heart and Circulatory Physiology 305, no. 5 (September 1, 2013): H716—H724. http://dx.doi.org/10.1152/ajpheart.00034.2013.
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Carotid endarterectomy has a long history in stroke prevention, yet controversy remains concerning optimal techniques. Two methods frequently used are endarterectomy with patch angioplasty (CEAP) and eversion endarterectomy (CEE). The objective of this study was to compare hemodynamics-related stress and strain distributions between arteries repaired using CEAP and CEE. Mathematical models were based on in vivo three-dimensional arterial geometry, pulsatile velocity profiles, and intraluminal pressure inputs obtained from 16 patients with carotid artery disease. These data were combined with experimentally derived nonlinear, anisotropic carotid artery mechanical properties to create fluid-structure interaction models of CEAP and CEE. These models were then used to calculate hemodynamic parameters thought to promote recurrent disease and restenosis. Combining calculations of stress and strain into a composite risk index, called the integral abnormality factor, allowed for an overall comparison between CEAP and CEE. CEE demonstrated lower mechanical stresses in the arterial wall, whereas CEAP straightened the artery and caused high stress and strain concentrations at the suture-artery interface. CEAP produced a larger continuous region of oscillatory, low-shear, vortical flow in the carotid bulb. There was a more than two-fold difference in the integral abnormality factor, favoring CEE. In conclusion, in a realistically simulated carotid artery, fluid-structure interaction modeling demonstrated CEE to produce less mechanical wall stress and improved flow patterns compared with CEAP. Clinical validation with larger numbers of individual patients will ultimately be required to support modeling approaches to help predict arterial disease progression and comparative effectiveness of reconstruction methods and devices.
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Horr, Amir M., Richard Kertz, and Michael Just. "Numerical Damage Modelling of Aluminium Alloys for Wide Range of Stress Triaxiality." Materials Science Forum 794-796 (June 2014): 646–51. http://dx.doi.org/10.4028/www.scientific.net/msf.794-796.646.
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There have been many efforts to investigate and develop a mechanical plasticity, damage and failure models for metal alloys in the last couple of decades. These models (single and multi-damage parameters) are generally based on energy and constitutive equations to simulate the fracture and failure processes in metal alloys. The conventional fracture mechanics theory and its applications have been successfully employed to study fracture and failure processes. However, these methods have serious short comes in predicting the damage and failure in metal alloys where the fracture is dominated by the presence of defects like micro-voids (and their growth, nucleation and coalescence), oxides and inclusions. In the present study, following the in-depth study of damage initiation and progression in aluminium alloys, a frame work has been setup to develop a numerical model for damage accumulation. Based on the existing phenomenological damage theory, a mathematical basis for damage initiation and also damage accumulation under wide range of stress triaxiality (including near pure shear) has been developed. The damage model has been checked and verified using a result of experimental-simulation comparative study. The experiments have been carried out using samples made from squeezed and high pressure casting step plates. One of the main contributions of this paper is to show the advantages of using plasticity-based modified damage models to investigate the damage accumulation in cast aluminium alloys.
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Tekin, Gülçin, and Fethi Kadıoğlu. "Viscoelastic Behavior of Shear-Deformable Plates." International Journal of Applied Mechanics 09, no. 06 (September 2017): 1750085. http://dx.doi.org/10.1142/s1758825117500855.
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The purpose of this study is to extend a new mixed-type finite element (MFE) model, developed earlier by the present authors for the analysis of viscoelastic Kirchhoff plates [Aköz, A. Y., Kadıoğlu, F. and Tekin, G. [2015] “Quasi-static and dynamic analysis of viscoelastic plates”, Mechanics of Time-Dependent Materials 19(4), 483–503], to study the quasi-static and dynamic responses of first-order shear-deformable (FSD) linear viscoelastic Mindlin–Reissner plates. In this context, various viscoelastic material models are discussed for the plate structure to read from them possible patterns of viscoelastic behavior. The developed MFE named VPLT32 is C0-continuous four-node linear isoparametric plate element with eight degrees of freedom per node. Hereditary integral form of the constitutive law with constant Poisson’s ratio is used. A new functional in the Laplace–Carson domain suitable for MFE formulation in the same domain is developed by employing Gâteaux differential (GD) method. The unique aspects of this study and the possible contributions of the proposed method to the literature can be summarized as follows: by using this new functional, moment and shear force values that are important for engineers can be obtained directly without any mathematical operation. In addition, geometric and dynamic boundary conditions can be obtained easily and a field variable can be included to the functional systematically. Moreover, shear-locking problem can be eliminated by using the GD method. Dubner and Abate numerical Laplace inversion technique is adopted to transform the obtained solution from the Laplace–Carson domain into the real-time domain. A set of numerical examples are presented not only to demonstrate the validity and accuracy of the proposed MFE formulation but also to examine the effects of load, geometry and material parameters on the viscoelastic response of FSD Mindlin–Reissner plates and to give a better insight into time-dependent behavior of engineering thick plate problems.
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Shapovalova, Mariya Ihorivna, and Oleksii Oleksandrovich Vodka. "Two-level mathematical models for determining the stress state and life plate with a hole." Bulletin of the National Technical University «KhPI» Series: Dynamics and Strength of Machines, no. 1 (December 31, 2021): 55–59. http://dx.doi.org/10.20998/2078-9130.2021.1.234843.
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Modern trends in the development of mechanical engineering and other industries related to the production of materials and structures with a given set of physical, mechanical, and technological properties are aimed at reducing material consumption, energy consumption, increasing accuracy, reliability, and competitiveness of the manufactured product. Therefore, the creation of mathematical methods for assessing the stress state of structural elements based on the analysis of the elastic characteristics of a material, taking into account the peculiarities of its internal microstructure, is an actual task. The considered algorithm includes the following stages: identification of strength parameters using data obtained from images of the material microstructure; study of the stress-strain state of the model based on the variational-difference finite element method; formation of a system of linear algebraic equations for solving the problem of analyzing the elastic properties of a material using the plane problem of the theory of elasticity; construction of the material yield surface for a series of tests based on the strength criteria of composite materials, taking into account the different resistance of the material under tensile and compressive loads. Based on the developed mathematical model, the SSS and the yield surface of the plate with a hole are estimated. Structural analysis is performed at the macro and micro levels. The occurrence of plastic deformations at the micro-level can lead to the development of cracks and structural damage at the macro level. As a result of the study, the probability of plastic deformation in the plate is determined, and the critical zones of the model are established. The practical significance of the results obtained is to create an approach to assessing the mechanical properties of a material, such as elastic modulus, shear modulus, Poisson's ratio, and their probabilistic characteristics following the internal material structure. The proposed approach contributes to the expansion of knowledge about the material and allows to increase the valuable information obtained by modeling. To assess the probability of plastic deformations, the generated method uses the entire set of probabilistic characteristics of the yield surface.
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Wang, Zhipeng, Guoli Zhang, Youxin Zhu, Liqing Zhang, Xiaoping Shi, and Weiwei Wang. "Theoretical analysis of braiding strand trajectories and simulation of three-dimensional parametric geometrical models for multilayer interlock three-dimensional tubular braided preforms." Textile Research Journal 89, no. 19-20 (February 13, 2019): 4306–22. http://dx.doi.org/10.1177/0040517519826888.
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Multilayer interlock three-dimensional (3D) tubular braided composites have been widely used in propeller blades, high pressure pipelines, rocket nose cones and engine nozzles owing to prominent interlaminar shear properties, reliable damage tolerance and outstanding torsion performance. The prediction of the mechanical properties and the design of the fabric structures for the 3D braided composites are dependent on the trajectory distribution of strands and the geometrical model of the braided structure. This paper aims to build theoretical models for the braiding strand trajectories and presents a creative method to establish the parametric geometrical models for the multilayer interlock 3D tubular braided structures. Firstly, mathematical models of braiding strand trajectories are derived based on the analysis for the characteristics of carrier paths, the interlacing and interlocking of braided structures and the motion of braiding strands. The mathematical models are then developed to establish parametric expressions for multilayer interlock 3D tubular braided structures by the advanced development of UG NX®. In addition, the models of corresponding braiding strand trajectories and braiding structures can be obtained automatically in the simulation environment with the modification of design parameters. Finally, the established models are compared with the carbon fiber braided specimen. The results show that the innovative parametric geometric models of the multilayer interlock 3D tubular braided structures accurately describe the key characteristics of the preform.
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Nauman, Eric A., C. Mark Ott, Ed Sander, Don L. Tucker, Duane Pierson, James W. Wilson, and Cheryl A. Nickerson. "Novel Quantitative Biosystem for Modeling Physiological Fluid Shear Stress on Cells." Applied and Environmental Microbiology 73, no. 3 (December 1, 2006): 699–705. http://dx.doi.org/10.1128/aem.02428-06.
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ABSTRACT The response of microbes to changes in the mechanical force of fluid shear has important implications for pathogens, which experience wide fluctuations in fluid shear in vivo during infection. However, the majority of studies have not cultured microbes under physiological fluid shear conditions within a range commonly encountered by microbes during host-pathogen interactions. Here we describe a convenient batch culture biosystem in which (i) the levels of fluid shear force can be varied within physiologically relevant ranges and quantified via mathematical models and (ii) large numbers of cells can be planktonically grown and harvested to examine the effect of fluid shear levels on microbial genomic and phenotypic responses. A quantitative model based on numerical simulations and in situ imaging analysis was developed to calculate the fluid shear imparted by spherical beads of different sizes on bacterial cell cultures grown in a rotating wall vessel (RWV) bioreactor. To demonstrate the application of this model, we subjected cultures of the bacterial pathogen Salmonella enterica serovar Typhimurium to three physiologically-relevant fluid shear ranges during growth in the RVW and demonstrated a progressive relationship between the applied fluid shear and the bacterial genetic and phenotypic responses. By applying this model to different cell types, including other bacterial pathogens, entire classes of genes and proteins involved in cellular interactions may be discovered that have not previously been identified during growth under conventional culture conditions, leading to new targets for vaccine and therapeutic development.
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Clayton, Erik H., Guy M. Genin, and Philip V. Bayly. "Transmission, attenuation and reflection of shear waves in the human brain." Journal of The Royal Society Interface 9, no. 76 (June 12, 2012): 2899–910. http://dx.doi.org/10.1098/rsif.2012.0325.
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Traumatic brain injuries (TBIs) are caused by acceleration of the skull or exposure to explosive blast, but the processes by which mechanical loads lead to neurological injury remain poorly understood. We adapted motion-sensitive magnetic resonance imaging methods to measure the motion of the human brain in vivo as the skull was exposed to harmonic pressure excitation (45, 60 and 80 Hz). We analysed displacement fields to quantify the transmission, attenuation and reflection of distortional (shear) waves as well as viscoelastic material properties. Results suggest that internal membranes, such as the falx cerebri and the tentorium cerebelli, play a key role in reflecting and focusing shear waves within the brain. The skull acts as a low-pass filter over the range of frequencies studied. Transmissibility of pressure waves through the skull decreases and shear wave attenuation increases with increasing frequency. The skull and brain function mechanically as an integral structure that insulates internal anatomic features; these results are valuable for building and validating mathematical models of this complex and important structural system.
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Aizikovich, S. M., L. I. Krenev, and I. S. Trubchik. "Stresses at the Interface between the Functionally Graded Coating and the Elastic Half-Space Caused by Spherical Indentation." Key Engineering Materials 345-346 (August 2007): 833–36. http://dx.doi.org/10.4028/www.scientific.net/kem.345-346.833.
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Recent advances in nanotechnology have revealed numerous new methods of manufacturing functionally graded coatings and materials, but progress in this field is limited by the lack of knowledge about the mechanical behavior of such structures. Existing models of the mechanics of layered structures are not generally adequate for this purpose, since functionally graded structures can exhibit both qualitative and quantitative behavioral differences in comparison with homogeneous or layered structures, particularly if there is a significant gradient of elastic properties in the coating. In applications, interest is focused mainly on the deformation fields and stresses inside the inhomogeneous material caused by the contact tractions. Stresses at the interface between the functionally graded coating and the elastic half-space are of particular interest because of their influence on the propagation of cracks and other defects on this interface. Shear stresses at this interface associated with rapid variation in elastic properties with depth are particularly dangerous because of potential delaminations. In their work the authors: • develop a precise mathematical model and of the computational methods which makes it possible to achieve stable numerical results while analyzing the mechanical properties of functionally graded coatings; • study the variation effect in elastic properties on the maximum stresses in the surface layers of materials with functionally graded coatings caused by indentation.
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Deng, Wubing, and Igor B. Morozov. "Solid viscosity of fluid-saturated porous rock with squirt flows at seismic frequencies." GEOPHYSICS 81, no. 4 (July 2016): D395—D404. http://dx.doi.org/10.1190/geo2015-0406.1.
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We have developed a macroscopic model for a two-phase medium (solid porous rock frame plus saturating pore fluid) with squirt flows based on Lagrangian continuum mechanics. The model focuses on improved physics of rock deformation, including explicit differential equations in time domain, causality, linearity, frequency-independent parameters with clear physical meanings, and an absence of mathematical internal or memory variables. The approach shows that all existing squirt-flow models can be viewed as microscopic models of viscosity for solid rock. As in existing models, the pore space is differentiated into compliant and relatively stiff pores. At lower frequencies, the effects of fluid flows within compliant pores are described by bulk and shear solid viscosities of the effective porous frame. Squirt-flow effects are “Biot consistent,” which means that there exists a viscous coupling between the rock frame and the fluid in stiff pores. Biot’s poroelastic effects associated with stiff porosity and global flows are also fully included in the model. Comparisons with several squirt-flow models show good agreement in predicting wave attenuation to approximately 1 kHz frequencies. The squirt-flow viscosity for sandstone is estimated in the range of [Formula: see text], which is close to field observations. Because of its origins in rigorous mechanics, the model can be used to describe any wavelike and transient deformations of heterogeneous porous media or finite bodies encountered in many field and laboratory experiments. The model also leads to new numerical algorithms for wavefield modeling, which are illustrated by 1D finite-difference waveform modeling.
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Paimushin, V. N., V. A. Firsov, and V. M. Shishkin. "MATHEMATICAL MODELING OF THE VIBRATIONS PROPAGATION IN THIN-WALL FRAMEWORK STRUCTURES. 1. BASIC RELATIONS AND ANALYTICAL SOLUTIONS OF TYPICAL PROBLEMS." Problems of Strength and Plasticity 84, no. 2 (2022): 207–24. http://dx.doi.org/10.32326/1814-9146-2022-84-2-207-224.
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The design features of the of thin-walled aerospace, shipbuilding, etc. structures in the form of a load-bearing frame sheathed with thin-walled panels, walls, bulkheads, etc. are discussed. Variants of constructive coupling of the specified thin-walled panels with supporting elements of the load-bearing frame and methods for their mathematical description in the classical mechanics of a deformable solid body are considered. It is proposed, without distorting the physical picture of the dynamic behavior of thin-walled panels, to present them in the form of multisupport thin bars resting on rigid elements of the load-bearing frame along part of their front surface. By the example of a plane dynamic problem of the mechanics of a bar with a fixed section of finite length on one of the front surfaces, it is shown that in the study of deformation processes, taking into account the compliance of the fixed section, it is necessary to introduce the concept of transformation of the stress-strain state parameters and the mathematical models used to describe them. Such a transformation takes place when crossing the border from an unfixed section to a fixed one (from a fixed to an unfixed one). Within the framework of the classical Kirchhoff–Love model, it is impossible to take into account the compliance of the fixed section of the bar, and when using the simplest refined shear model of S.P. Timoshenko, such accounting is possible when fixing the length only on one of the front surfaces. In particular, previously discovered and not described in the scientific literature phenomenon of the vibrations transmission through the support joints, regardless of their design, is carried out due to the transformation of the stress-strain state of the dynamically loaded section of the bar into longitudinal-shear vibration modes of the bar in the clamped area, followed by their retransformation into bending vibrations of the adjacent span. Within the framework of S.P. Timoshenko model, the main resolving equations are constructed, and the kinematic and force conditions for conjugation of fixed and non-fixed sections of the bar are formulated. On the basis of the developed mathematical model, exact analytical solutions of typical problems are constructed, confirming the transmission of vibration through the clamped sections of the bar due to the deformability of the marked sections. A significant increase of transverse shear stresses level in the clamped section of the bar in the vicinity of the junction of the unfixed section with the fixed one is revealed.
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McGinty, R. D., T. B. Rhyne, and S. M. Cron. "Analytical Solution for the Stresses Arising in +/− Angle Ply Belts of Radial Tires." Tire Science and Technology 36, no. 4 (December 1, 2008): 244–74. http://dx.doi.org/10.2346/1.2999704.
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Abstract Stresses arising in the belts of radial ply tires, particularly those at the belt edge, are known to be critical to tire durability. Belt edge stresses are commonly calculated using finite element (FE) methods that provide estimates of the levels but do not necessarily give significant insight into the underlying mechanics. In contrast, analytical models can provide physical insight into the mechanisms affecting tire durability but are currently incomplete due to the challenges faced in obtaining closed-form mathematical solutions. Nevertheless, analytical solutions remain important to tire design and development because they can expose the entire design space, show the mathematical relationships between the variables, and allow rapid parameter studies. This work develops an analytical description of the belt deformations and stresses, particularly at the belt edge. The formulation captures all the first-order mechanics pertinent to finite width, antisymmetric +/− angle belt packages present in radial tires. It incorporates interply shear stresses already recognized in the literature and adds to that a new mechanism controlling the interaction of the plies via a Poisson effect. The analytical model is validated by comparison to FE simulations and is also contrasted with a classical analytical model in the literature. The design space for the belt composite is then explored by parameter variation. Finally, since all these solutions depend on homogenization of the belt layers, the analytical solution is compared to a FE model of discrete cables embedded in rubber to explore the accuracy of the homogenization step.
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Liu, Fengjie, Monan Wang, and Yuzheng Ma. "Multiscale modeling of skeletal muscle to explore its passive mechanical properties and experiments verification." Mathematical Biosciences and Engineering 19, no. 2 (2021): 1251–79. http://dx.doi.org/10.3934/mbe.2022058.
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<abstract> <p>The research of the mechanical properties of skeletal muscle has never stopped, whether in experimental tests or simulations of passive mechanical properties. To investigate the effect of biomechanical properties of micro-components and geometric structure of muscle fibers on macroscopic mechanical behavior, in this manuscript, we establish a multiscale model where constitutive models are proposed for fibers and the extracellular matrix, respectively. Besides, based on the assumption that the fiber cross-section can be expressed by Voronoi polygons, we optimize the Voronoi polygons as curved-edge Voronoi polygons to compare the effects of the two cross-sections on macroscopic mechanical properties. Finally, the macroscopic stress response is obtained through the numerical homogenization method. To verify the effectiveness of the multi-scale model, we measure the mechanical response of skeletal muscles in the in-plane shear, longitudinal shear, and tensions, including along the fiber direction and perpendicular to the fiber direction. Compared with experimental data, the simulation results show that this multiscale framework predicts both the tension response and the shear response of skeletal muscle accurately. The root mean squared error (RMSE) is 0.0035 MPa in the tension along the fiber direction; The RMSE is 0.011254 MPa in the tension perpendicular to the fiber direction; The RMSE is 0.000602 MPa in the in-plane shear; The RMSE was 0.00085 MPa in the longitudinal shear. Finally, we obtained the influence of the component constitutive model and muscle fiber cross-section on the macroscopic mechanical behavior of skeletal muscle. In terms of the tension perpendicular to the fiber direction, the curved-edge Voronoi polygons achieve the result closer to the experimental data than the Voronoi polygons. Skeletal muscle mechanics experiments verify the effectiveness of our multiscale model. The comparison results of experiments and simulations prove that our model can accurately capture the tension and shear behavior of skeletal muscle.</p> </abstract>
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Luo, Yi, Hong Ye, Cheng Zhi Xiong, Lin Liu, and Xu Wei Lv. "Resistance Spot Welding Process of Galvanized Steel Sheet Based on Regression Modeling." Materials Science Forum 610-613 (January 2009): 681–86. http://dx.doi.org/10.4028/www.scientific.net/msf.610-613.681.
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The resistance spot welding process of galvanized steel sheet used in the body manufacturing of family car was studied, and the indexes of nugget geometry and tensile-shear strength of spot welds were tested. Four process parameters, namely welding current, electrode force, welding current duration and preheat current, and interactions among them were regarded as factors impacting indexes. Method using in mathematical models developing was nonlinear multiple orthogonal regression assembling design, which was optimized by the technology of variance analysis. The experimental results showed that more accurate prediction on nugget size and mechanical properties of spot welds can be obtained by the models optimized. With these prediction results, the optimization of welding process also was realized by the analysis to effect of the parameters and interactions on the welding quality.
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Sujan, D., T. K. Piaw, and Dereje Engida Woldemichael. "Thermo-Mechanical Stress Analysis in Electronic Packaging with Continuous and Partial Bond Layer." Applied Mechanics and Materials 465-466 (December 2013): 50–54. http://dx.doi.org/10.4028/www.scientific.net/amm.465-466.50.
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Interfacial stress due to thermal mismatch in layered structure has been considered as one of the major causes of mechanical failure in electronic packaging. The mismatch due to the differences in coefficient of thermal expansion (CTE) of the materials in multi-layered structure may induce severe stress concentration to the electronic composites namely interfacial delamination and die cracking. Therefore, the studies and evaluation of interfacial stress in electronic packaging become significantly important for optimum design and failure prediction of the electronic devices. The thermal mismatch shear stress for bi-layered assembly can be analyzed by using the mathematical models based on beam theory. In this study, Finite Element Method (FEM) simulation was performed to an electronic package by using ANSYS. The shear stress growth behavior at the interface of the bonded section was studied with the considerations of continuous and partial bond layers in the interfaces. Based on the analysis, it can be observed that the partial bond layer with small center distances can be simplified as a continuous bond layer for bi-layered shearing stress model analysis.
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Kondratieva, Lidiia, Aleksandr Kuznetsov, and Ekaterina Moiseyeva. "REVIEW OF THE ANALYTICAL ASSESSMENT METHOD OF FINDING THE SEISMIC AND EXTREME LOAD RESILIENCE OF SHEAR LINKS." Architecture and Engineering 5, no. 4 (2020): 60–64. http://dx.doi.org/10.23968/2500-0055-2020-5-4-60-64.
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Introduction: This paper reviews the analytical method of assessing the seismic and extreme load resistance of buildings with a complex macrostructure that includes elastic-plastic inserts operating in shear. Methods: We analyze a number of studies that rationalize the choice of models for simulating complex elastic-plastic deformation in a mechanical system with several degrees of freedom, as well as studies that review the durability and resilience of buildings with a complex macrostructure based on non-linear shear links when subjected to dynamic and extreme impact. We also consider the methods of structural analysis regarding buildings with elastic-plastic inserts, accounting for the plastic hinged joints of metal frames. Results: We apply the analytical method to linear and non-linear systems with n degrees of freedom. We propose a mathematical equation that describes the nature of shear link response to seismic and extreme loads. Our method makes it possible to obtain an analytical solution for structures with proportionate and disproportionate damping by using the direct integration algorithm. Discussion: Most structures with a broad range of construction material properties require a disproportionate damping model. In this study, we solve equations by using the direct integration algorithm based on disproportionate damping. Under high dynamic load, the reinforcement of shear inserts operates in a plastic state.
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Zhang, Pei, and Hai Qing. "On well-posedness of two-phase nonlocal integral models for higher-order refined shear deformation beams." Applied Mathematics and Mechanics 42, no. 7 (June 24, 2021): 931–50. http://dx.doi.org/10.1007/s10483-021-2750-8.
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AbstractDue to the conflict between equilibrium and constitutive requirements, Eringen’s strain-driven nonlocal integral model is not applicable to nanostructures of engineering interest. As an alternative, the stress-driven model has been recently developed. In this paper, for higher-order shear deformation beams, the ill-posed issue (i.e., excessive mandatory boundary conditions (BCs) cannot be met simultaneously) exists not only in strain-driven nonlocal models but also in stress-driven ones. The well-posedness of both the strain- and stress-driven two-phase nonlocal (TPN-StrainD and TPN-StressD) models is pertinently evidenced by formulating the static bending of curved beams made of functionally graded (FG) materials. The two-phase nonlocal integral constitutive relation is equivalent to a differential law equipped with two restriction conditions. By using the generalized differential quadrature method (GDQM), the coupling governing equations are solved numerically. The results show that the two-phase models can predict consistent scale-effects under different supported and loading conditions.
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Pasichnyk, S. S., and N. V. Bezrukavyi. "Increasing the 18-100 freight-car truck shear stiffness." Technical mechanics 2020, no. 3 (October 15, 2020): 91–98. http://dx.doi.org/10.15407/itm2020.03.091.
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Although a large number of truck models have been put into service on the 1520 mm gage railways over the past ten years, the problem of an insufficient shear stiffness of a freight car truck still remains topical. This problem is a consequence of attempts to keep a sufficient degree of unification of new truck models with the 18-100 truck because this greatly simplifies the introduction of new trucks and allows one to make the best use of the existing maintenance and repair infrastructure. However, this also results in that new designs inherit many drawbacks of the 18-100 truck. One of its critical drawbacks is a low connectedness in a horizontal plane, which reduces the critical speed and increases truck component wear. A solution to this problem may be an auxiliary stiffening frame. This paper presents a new design of an auxiliary stiffening frame for the 18-100 truck. The design increases the truck shear stiffness, thus improving freight car dynamic performance and service life. Mathematical simulation, oscillation theory, and elasticity theory methods were used to design an auxiliary stiffening frame installable between the 18-100 truck side frames without any significant changes in the freight car basic design. The physical and mechanical properties of the auxiliary stiffening frame’s structural materials were selected. Loads on the auxiliary stiffening frame were determined and then used in the calculation of the stresses that develop therein in motion. It was found that the proposed auxiliary stiffening frame with resilient polyurethane inserts increases the truck shear stiffness by 0.5 MN/m. The proposed improved design of the 18-100 truck increases its shear stiffness, improves freight car dynamic and operational performance, and reduces truck component wear. Besides, the auxiliary stiffening frame is simple in design. Because of this, its introduction will bring considerable economic benefits.
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Gholami, R., R. Ansari, and Y. Gholami. "Nonlocal large-amplitude vibration of embedded higher-order shear deformable multiferroic composite rectangular nanoplates with different edge conditions." Journal of Intelligent Material Systems and Structures 29, no. 5 (August 4, 2017): 944–68. http://dx.doi.org/10.1177/1045389x17721377.
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Based on the nonlocal elasticity theory, a unified nonlocal, nonlinear, higher-order shear deformable nanoplate model is developed to investigate the size-dependent, large-amplitude, nonlinear vibration of multiferroic composite rectangular nanoplates with different boundary conditions resting on an elastic foundation. By considering a unified displacement vector and using von Kármán’s strain tensor, the strain–displacement components are obtained. Using coupled nonlocal constitutive relations, the coupled ferroelastic, ferroelectric, ferromagnetic, and thermal properties of multiferroic composite materials and small-scale effect are taken into account. The electric and magnetic potential distributions in the nanoplate are calculated via Maxwell’s electromagnetic equations. Furthermore, Hamilton’s principle is utilized to obtain the mathematical formulation associated with the coupled governing equations of motions and boundary conditions. The developed model enables us to consider the effects of rotary inertia and transverse shear deformation without using any shear correction factor. Also, it can be degenerated to the models based on the Kirchhoff and existing shear deformation plate theories. To solve the large-amplitude vibration problem, an efficient multistep numerical solution approach is utilized. Effects of various important parameters such as the type of the plate theory, and parameters of nonlocality and coupled fields on the nonlinear frequency response are investigated.
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Franchi, Franca, Barbara Lazzari, and Roberta Nibbi. "Viscoelastic type magnetic effects and self-gravity on the propagation of MHD waves." Meccanica 55, no. 11 (October 22, 2020): 2199–214. http://dx.doi.org/10.1007/s11012-020-01252-9.
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Abstract We take up the challenge to explain the correlation between the Jeans instability topic towards star formation within the accelerated expansion of universe and the role of torsional shear-like Alfven waves in triggering the formation of network patterns, by proposing new mathematical models for self-gravitating interstellar non ideal MHD plasmas. The diffusion of the gravitational field is included via a parabolic Einstein’s equation with the cosmological constant, whereas anomalous resistive features are described through non ideal Ohm’s laws incorporating inertia terms, to account of relaxation and retardation magnetic responses. We perform a spectral analysis to test the stability properties of the novel constitutive settings where dissipative and elastic devices act together, by emphasizing the differences with previous models. As a main result, we highlight the definition of a lower critical threshold, here called the Jeans-Einstein wavenumber, against collapse formation towards the formation of longitudinal gravito-magneto-sonic waves and transverse non gravitational Alfven waves exhibiting larger effective wavespeeds, due to the hyperbolic-parabolic diffusion of the magnetic field. Consequently shorter collisional times are allowable so, beyond the plasma-beta, another interesting key point is the definition of the Ohm number to revisit the timescale topic, towards reviewed Reynolds and Lundquist numbers able to better capture the microphysical phenomena of Magnetic Reconnection in narrow diffusion regimes.
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Öğülmüş Demircan, Fadime, İbrahim Yücedağ, and Metin Toz. "A novel mathematical model including the wetness parameter as a variable for prevention of pressure ulcers." Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine 236, no. 3 (October 26, 2021): 427–37. http://dx.doi.org/10.1177/09544119211048557.
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Pressure ulcers are injuries caused by external conditions such as pressure, friction, shear, and humidity resulting from staying in the same position for a long time in bedridden patients. It is a serious problem worldwide when assessed in terms of hospital capacity, nursing staff employment and treatment costs. In this study, we developed a novel mathematical model based on one of our previous models to prevent pressure ulcers or delay injuries. The proposed model uses a human thermal model that includes skin temperature, hypothalamus temperature, regional perspiration coefficient, and unconsciously loss of water amount. Moreover, in our model, we defined a variable wetness parameter in addition to the parameters, pressure, temperature, and humidity. The proposed model is mathematically defined in detail and tested for a wide range of parameters to show the model’s effectiveness in determining the pressure ulcer formation risk. The model is also compared with a model from the literature that based on only the general parameters, pressure, temperature, and humidity. The obtained results showed that the model determines the risk of the occurrence of the pressure ulcer more precisely than the compared one.