Journal articles on the topic 'Deformation (Mechanics) Mathematical models'
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Xin, Jiaxing, Jinzhong Chen, Xiaolong Li, Renyang He, and Hongwu Zhu. "A prediction model for oil and gas pipeline deformation based on ACM inspection signal waveforms." Insight - Non-Destructive Testing and Condition Monitoring 64, no. 10 (October 1, 2022): 573–81. http://dx.doi.org/10.1784/insi.2022.64.10.573.
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Deformation is one of the leading causes of oil and gas pipeline accidents, affecting pipeline transportation efficiency and operational safety. This paper proposes a pipeline deformation detection method and prediction models based on alternating current magnetisation (ACM) technology. Firstly, the mechanism of pipeline deformation detection based on ACM technology is introduced and mathematical models are proposed to evaluate the deformation length and height using magnetic detection signals. Next, finite element models of detection signals for deformations with various lengths and heights are analysed and original signal waveforms are obtained. Furthermore, linear and polynomial fitting mathematical models are developed to invert the deformation length and height using the measured peak signal and L' (distorted signal length) value. Finally, experiments are conducted to demonstrate that the length and depth of a deformation can be estimated by linear and polynomial models with tolerable errors. The proposed approach combining ACM and a prediction model is verified to size deformation in pipeline inspection quantitatively.
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SACHSE, FRANK B., GUNNAR SEEMANN, MATTHIAS B. MOHR, and ARUN V. HOLDEN. "MATHEMATICAL MODELING OF CARDIAC ELECTRO-MECHANICS: FROM PROTEIN TO ORGAN." International Journal of Bifurcation and Chaos 13, no. 12 (December 2003): 3747–55. http://dx.doi.org/10.1142/s0218127403008910.
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Mathematical models of cardiac anatomy and physics provide information, which help to understand structure and behavior of the heart. Miscellaneous cardiac phenomena can only be adequately described by combination of models representing different aspects or levels of detail. Coupling of these models necessitates the definition of appropriate interfaces. Adequateness and efficiency of interfaces is crucial for efficient application of the combined models. In this work an integrated model is presented consisting of several models interconnected by interfaces. The integrated model allows the reconstruction of macroscopic electro-mechanical processes in the heart. The model comprises a three-dimensional are of left ventricular anatomy represented as truncated ellipsoid. The integrated model includes electrophysiological, tension development and elastomechanical models of myocardium at levels of single cell, proteins, and tissue patches, respectively. The model is exemplified by simulations of extracorporated left ventricle of small mammals. These simulations yield temporal distributions of electrophysiological parameters as well as descriptions of electrical propagation and mechanical deformation. The simulations show characteristic macroscopic ventricular function resulting from the interplay between cellular electrophysiology, electrical excitation propagation, tension development, and mechanical deformation.
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Erasov, V. S., E. I. Oreshko, and A. N. Lutsenko. "MULTILEVEL LARGE-SCALE COMPLEX RESEARCH OF DEFORMATION OF METAL MATERIALS." Aviation Materials and Technologies, no. 1 (2022): 129–42. http://dx.doi.org/10.18577/2713-0193-2022-0-1-129-142.
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The paper considers the theoretical and experimental questions connected with researches of elastic and plastic deformation of metal materials. The article shows that joint multilevel large-scale study performed by physics-mechanics and material engineers of the patterns connecting characteristics of stress-strain state with parameters of a structural condition of a metal material will allow to develop modern physical and mathematical models of a material. For this purpose in-depth study of the shift deformations forming plastic properties of a material and processes formation of defects and a new free surface is necessary. The paper presents the examples of such a research, and provides methods of analysis of structure and physical and mechanical characteristics at different structural levels of a polycrystalline metal material.
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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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Krysko, A. V., J. Awrejcewicz, K. S. Bodyagina, and V. A. Krysko. "Mathematical modeling of planar physically nonlinear inhomogeneous plates with rectangular cuts in the three-dimensional formulation." Acta Mechanica 232, no. 12 (November 16, 2021): 4933–50. http://dx.doi.org/10.1007/s00707-021-03096-0.
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AbstractMathematical models of planar physically nonlinear inhomogeneous plates with rectangular cuts are constructed based on the three-dimensional (3D) theory of elasticity, the Mises plasticity criterion, and Birger’s method of variable parameters. The theory is developed for arbitrary deformation diagrams, boundary conditions, transverse loads, and material inhomogeneities. Additionally, inhomogeneities in the form of holes of any size and shape are considered. The finite element method is employed to solve the problem, and the convergence of this method is examined. Finally, based on numerical experiments, the influence of various inhomogeneities in the plates on their stress–strain states under the action of static mechanical loads is presented and discussed. Results show that these imbalances existing with the plate’s structure lead to increased plastic deformation.
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Zhuravlev, G. M., A. E. Gvozdev, S. V. Sapozhnikov, S. N. Kutepov, and E. V. Ageev. "DECISIONS ON STATISTICAL MODELS IN QUALITY CONTROL OF PRODUCTS." Proceedings of the Southwest State University 21, no. 5 (October 28, 2017): 78–92. http://dx.doi.org/10.21869/2223-1560-2017-21-5-78-92.
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Development of methods for registration, description and analysis of statistical experimental data, obtained by monitoring mass random phenomena is the subject of a special science - mathematical statistics. All tasks of mathematical statistics concerns the treatment of observations of mass random phenomena, but depending on the nature of the solved practical question and amount of available experimental material these tasks can take a particular form. One of the main objectives of mathematical statistics is to develop methods of studying mass phenomena or processes on the basis of the relatively small number of observations or experiments. These methods have their scientific justification, his theory, called the theory of samples. The aim of this work is to build mathematical models of influence of various factors on a single number using the method of multifactor experiment planning, and their use results in the appointment of modes of technological operations. To study processes incomplete hot deformation uses a complex viscoplastic model of the environment, the mechanical properties which are characterized by a yield stress and viscosity. The yield strength depends on temperature and strain rate. On this basis, was carried out processing of experimental data by the method of multifactor experiment planning and statistical treatment of experimental data by definition of the yield strength depending on temperature and speed of deformation of steel U12A. From the analysis of the obtained regression equations, we can conclude that the most highly specific force depends on temperature. Regression equations mathematically describe the mutual influence of technological factors on yield strength and specific strength, in addition they allow you to correctly set processing modes that yield products of the required quality.
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Bagrii, O. V. "Plane problem of discrete environment mechanics." Problems of Tribology 27, no. 2/104 (June 25, 2022): 104–11. http://dx.doi.org/10.31891/2079-1372-2022-104-2-104-111.
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Many engineering problems related to the design of structures and machines, the mathematical description of technological processes, etc., are reduced to the need to solve a plane problem for materials with a significant effect of internal friction on their deformation. Such materials include a large class of materials in which the compressive strength is greater than tensile. These are composite materials, concretes, rocks, soils, granular, loose, highly fractured materials, as well as structurally heterogeneous materials in which rigid and strong particles are interconnected by weaker layers. The laws of deformation and destruction of such materials differ significantly from elastic ones. A feature of these laws is an increase in resistance to shear deformations and an increase in the strength of materials with an increase in the magnitude of compressive stresses. This is associated with the influence of internal Coulomb friction on the process of their deformation in the limiting and boundary stages.
The need to formulate and solve a special boundary value problem for materials with significant internal friction is because the results of solving problems using models of elasticity and plasticity differ significantly from experimental data. The difference increases when approaching the limiting state of discrete materials and depends significantly on the structure of the material and operating conditions.
The boundary value problem of the mechanics of a deformable solid is formulated as a system of equations of three types: static, geometric, and physical. For all linear and physically nonlinear problems, provided the deformations are small, the first two groups of equations remain the same. Thus, these differences can be attributed to the inconsistency of the accepted in the calculations of physical relations "stress - strain" and the real laws of deformation of these materials, which are more complex rheological objects than structurally homogeneous solids, liquids or gases.
The article uses an approach where the material is immediately considered as quasi-continuous, and the physical equations are based on the experimentally obtained relationships between the invariants of the stress and strain tensors, which consider the influence of both molecular connectivity and internal Coulomb friction.
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Feng, Rui, Youlin Bao, Yongshun Ding, Minghe Chen, Yan Ge, and Lansheng Xie. "Three different mathematical models to predict the hot deformation behavior of TA32 titanium alloy." Journal of Materials Research 37, no. 7 (April 4, 2022): 1309–22. http://dx.doi.org/10.1557/s43578-022-00532-2.
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Okuno, A., and H. B. Kingsbury. "Dynamic Modulus of Poroelastic Materials." Journal of Applied Mechanics 56, no. 3 (September 1, 1989): 535–40. http://dx.doi.org/10.1115/1.3176123.
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A simple mathematical formula is proposed to predict the fluid damping effects in poroelastic materials. Biot’s poroelasticity equations are solved to obtain the response of poroelastic materials undergoing harmonic tension-compression and bending deformation. Complex moduli of poroelastic material are explored from the response functions on basis of mathematical models. It is shown that the effects of material parameters, geometrical parameters, and flow boundary conditions on the fluid damping are predicted by simple mathematical formulas. Numerical results are presented and compared with those of other researchers.
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Bobkov, S. P., and I. V. Polishchuk. "Simulation and visualization of solid deformation upon impact." Vestnik IGEU, no. 2 (2020): 51–57. http://dx.doi.org/10.17588/2072-2672.2020.2.051-057.
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The use of adequate mathematical models to study the process of deformation of solids is an urgent issue for industrial engineering. It is known that under mechanical action the bodies are deformed and mechanical stresses arise in them, which, in turn, lead to destruction. Therefore, the simulation of deformation processes can be useful both in studying the issues of strength and reliability of equipment and for solving problems of fine grinding of solid fuels. Classical continuum models of continuum mechanics are useful for studying mechanical stresses in idealized environments and for bodies of regular shape. Their application in the analysis of heterogeneous structures and objects of complex shape encounters significant difficulties. In such cases, a number of simplifying assumptions have to be introduced, which reduces the adequacy of the models. A discrete model which considers a solid body as a set of local elements connected by elastic bonds is used in the research. A significant difference between the proposed approach and the one previously used is the following. In previous models, the separate local element of unit mass was a discretization step of space. In the new interpretation, the discretization step is consistent with the behavior of a system (set) of several interacting unit masses. An improved approach to the analysis of the process of deformation of a solid has been investigated. A model that allows studying not only axial deformations (compression – tension) but also the effects of changes in transverse dimensions (shear) has been proposed. It has been established that this approach to modeling can significantly simplify the visualization of the process at each step of the discrete time. The obtained results have made it possible to improve discrete approaches to simulation of solids deformation process. At the same time, it has become possible to model not only axial deformations (compression – tension), but also the effects of changes in transverse dimensions (shear). The discrete approach to modeling has enabled to significantly simplify the visualization of the process at each step of the discrete time. The study has shown that the discrete approach allows analyzing the stress state and visualizing the propagation of deformation waves in solids at free impact. The data on the propagation of elastic waves obtained by computer simulation coincide with the results of preceding physical experiments. The discrete approach does not create difficulties in analyzing the behavior of heterogeneous bodies of complex shape, since the design features are considered at the local level and do not require adjustment of the modeling algorithm.
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Topilnytskyy, Volodymyr, and Kostiantyn Kabanov. "Mathematical model of dynamics of vibrating systems working environments." Ukrainian Journal of Mechanical Engineering and Materials Science 8, no. 1 (2022): 44–50. http://dx.doi.org/10.23939/ujmems2022.01.044.
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Using the apparatus of the special periodic Ateb-functions in combination with the asymptotic methods of nonlinear mechanics, the nonlinear mathematical models of motion of working environment of the oscillation system, which dependences take into account resilient and viscid making tensions from descriptions of the deformation state of environment, her physical and mechanical properties and features of co-operation of environment with the oscillation system, are worked out. The nonlinear model for describing the dynamics of the working environment of oscillating systems is more flexible, because the nonlinearity index, which depends on the type of working load, significantly affects the results of the oscillating loading process. It allows us to take into account the type of load, and, accordingly, increase the level of adequacy of the constructed analytical model of the oscillatory process that needs to be investigated. Taking into account this model, the study of various processes in oscillating systems can be carried out, in particular in different modes of vibration processing.
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Kayumov, Rashit, and Inzilija Mukhamedova. "Mathematical model of the modified tissue deformation under stretching." E3S Web of Conferences 274 (2021): 11005. http://dx.doi.org/10.1051/e3sconf/202127411005.
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One of the effective methods for modifying natural and synthetic materials is a use of the flocking process. To analyze a quality of the modified fabrics, it is useful to have mathematical models describing a stress-strain state of the fabrics when exposed to various loads. A method has been developed for determining the stiffness characteristics of a flocked fabric based on the results of testing samples cut at different angles to the base at different tensile forces. This technique makes it possible to analyze the effect of flocking on the mechanical characteristics of the fabric. It was revealed that the theory of mixtures, when averaging the properties of the fabrics and glue with respect to thickness, does not allow determining the stiffness characteristics with acceptable accuracy. The limits of applicability of the theory of mixtures were determined when carrying out averaging of the mechanical characteristics with respect to the area of the flocked fabrics.
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Zhi, Xiang Cao, Jia Zhu Xue, and Xiu Li Cao. "The Research on Damage and Failture Mechanism of Drivepipe under Seismic Load." Advanced Materials Research 374-377 (October 2011): 2096–99. http://dx.doi.org/10.4028/www.scientific.net/amr.374-377.2096.
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Geological factors and engineering factors is a major factor to damage, the drivepipe deformation under pressure seismic load which used to establish mathematical model of the mechanical model can calculated the stress and strain analysis of the casing. The drivepipe damage to this article on the mechanism research on the mechanical model of drivepipe analysis under Seismic load, based on the drivepipe through the focus on the impact and stress damage to the mechanical method of drivepipe deformation studies, and the models of a drivepipe failure mechanism of the mechanical and mathematical are established, which will scientifically, accurately predict the damaged drivepipe.
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Krysko, A. V., J. Awrejcewicz, K. S. Bodyagina, M. V. Zhigalov, and V. A. Krysko. "Mathematical modeling of physically nonlinear 3D beams and plates made of multimodulus materials." Acta Mechanica 232, no. 9 (June 26, 2021): 3441–69. http://dx.doi.org/10.1007/s00707-021-03010-8.
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AbstractIn this work, mathematical models of physically nonlinear plates and beams made from multimodulus materials are constructed. Our considerations are based on the 3D deformation theory of plasticity, the von Mises plasticity criterion and the method of variable parameters of the theory of elasticity developed by Birger. The proposed theory and computational algorithm enable for solving problems of three types of boundary conditions, edge conditions and arbitrary lateral load distribution. The problem is solved by the finite element method (FEM), and its convergence and the reliability of the results are investigated. Based on numerical experiments, the influence of multimodulus characteristics of the material of the beam and the plate on their stress–strain states under the action of transverse loads is illustrated and discussed.
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Taghizadeh, D. M., and H. Darijani. "Mechanical Behavior Modeling of Hyperelastic Transversely Isotropic Materials Based on a New Polyconvex Strain Energy Function." International Journal of Applied Mechanics 10, no. 09 (November 2018): 1850104. http://dx.doi.org/10.1142/s1758825118501041.
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In this paper, the mechanical behavior of incompressible transversely isotropic materials is modeled using a strain energy density in the framework of Ball’s theory. Based on this profound theory and with respect to physical and mathematical aspects of deformation invariants, a new polyconvex constitutive model is proposed for the mechanical behavior of these materials. From the physical viewpoint, it is assumed that the proposed model is additively decomposed into three parts nominally representing the energy contributions from the matrix, fiber and fiber–matrix interaction where each of the parts should be presented in terms of the invariants consistent with the physics of the deformation. From the mathematical viewpoint, the proposed model satisfies the fundamental postulates on the form of strain energy density, specially polyconvexity and coercivity constraints. Indeed, polyconvexity ensures ellipticity condition, which in turn provides material stability and in combination with coercivity condition, guarantees the existence of the global minimizer of the total energy. In order to evaluate the performance of the proposed strain energy density function, some test data of incompressible transverse materials with pure homogeneous deformations are used. It is shown that there is a good agreement between the test data and the obtained results from the proposed model. At the end, the performance of the proposed model in the prediction of the material behavior is evaluated rather than other models for two representative problems.
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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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Cicci, Ludovica, Stefania Fresca, Stefano Pagani, Andrea Manzoni, and Alfio Quarteroni. "Projection-based reduced order models for parameterized nonlinear time-dependent problems arising in cardiac mechanics." Mathematics in Engineering 5, no. 2 (2022): 1–38. http://dx.doi.org/10.3934/mine.2023026.
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<abstract><p>The numerical simulation of several virtual scenarios arising in cardiac mechanics poses a computational challenge that can be alleviated if traditional full-order models (FOMs) are replaced by reduced order models (ROMs). For example, in the case of problems involving a vector of input parameters related, e.g., to material coefficients, projection-based ROMs provide mathematically rigorous physics-driven surrogate ROMs. In this work we demonstrate how, once trained, ROMs yield extremely accurate predictions (according to a prescribed tolerance) – yet cheaper than the ones provided by FOMs – of the structural deformation of the left ventricular tissue over an entire heartbeat, and of related output quantities of interest, such as the pressure-volume loop, for any desired input parameter values within a prescribed parameter range. However, the construction of ROM approximations for time-dependent cardiac mechanics is not straightforward, because of the highly nonlinear and multiscale nature of the problem, and almost never addressed. Our approach relies on the reduced basis method for parameterized partial differential equations. This technique performs a Galerkin projection onto a low-dimensional space for the displacement variable; the reduced space is built from a set of solution snapshots – obtained for different input parameter values and time instances – of the high-fidelity FOM, through the proper orthogonal decomposition technique. Then, suitable hyper-reduction techniques, such as the Discrete Empirical Interpolation Method, are exploited to efficiently handle nonlinear and parameter-dependent terms. In this work we show how a fast and reliable approximation of the time-dependent cardiac mechanical model can be achieved by a projection-based ROM, taking into account both passive and active mechanics for the left ventricle providing all the building blocks of the methodology, and highlighting those challenging aspects that are still open.</p></abstract>
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Barari, A., M. Omidvar, D. D. Ganji, and Abbas Tahmasebi Poor. "An Approximate Solution for Boundary Value Problems in Structural Engineering and Fluid Mechanics." Mathematical Problems in Engineering 2008 (2008): 1–13. http://dx.doi.org/10.1155/2008/394103.
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Variational iteration method (VIM) is applied to solve linear and nonlinear boundary value problems with particular significance in structural engineering and fluid mechanics. These problems are used as mathematical models in viscoelastic and inelastic flows, deformation of beams, and plate deflection theory. Comparison is made between the exact solutions and the results of the variational iteration method (VIM). The results reveal that this method is very effective and simple, and that it yields the exact solutions. It was shown that this method can be used effectively for solving linear and nonlinear boundary value problems.
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Han, Guomin, Hongbo Li, Yujin Liu, Jie Zhang, Ning Kong, Zhiyuan Hu, and Lei Liu. "A simplified mathematical model for total temperature rise calculation in non-oriented silicon steel cold rolling deformation zone." Metallurgical Research & Technology 119, no. 1 (December 20, 2021): 104. http://dx.doi.org/10.1051/metal/2021095.
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In tandem cold rolling, the control of the temperature of high-grade non-oriented silicon steel is a difficult problem for its large deformation resistance and the preheating procedure before rolling. And it is complicated to calculate the total temperature rise of rolling deformation zone due to the comprehensive influence of the plastic deformation heat, the friction heat and the contact heat loss. So, to precisely calculate the total temperature rise, firstly, based on the four classical cold rolling force formulas, the initial total temperature rise calculation models are established correspondingly by theoretically analyzing the temperature rise of deformation heat, the temperature rise of friction heat and the temperature drop of contact heat loss; then, the model based on the improved Lian rolling force formula is adopted, which leads to calculated best matching the measured temperature; finally, considering the complex formula calculation of the initial model, based on the influences of different rolling parameters on the total temperature rise, a simplified model for convenient calculation is proposed by the nonlinear regression analysis of the initial model calculation results and main rolling parameters, which is convenient for the actual application by the field technicians.
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Tyshkevich, Vladimir N., Alexander V. Sarazov, and Sergey V. Orlov. "Algorithm of Determination of Optimal Conditions for Low-Rigidity Prismatic Workpieces Flat Grinding." Key Engineering Materials 910 (February 15, 2022): 138–43. http://dx.doi.org/10.4028/p-9542bg.
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The flat grinding of low-rigidity prismatic workpieces side surfaces is investigated. Algorithm of determination of optimal conditions for low-rigidity prismatic workpieces flat grinding has been developed. The optimization of parameters in the range of allowable values is carried out with the view of ensuring the maximum process efficiency. Mathematical models for determination of maximum elastic deformation of prismatic workpieces when fixing and machining are presented.
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Oden, J. T., T. L. Lin, and J. M. Bass. "A Finite Element Analysis of the General Rolling Contact Problem for a Viscoelastic Rubber Cylinder." Tire Science and Technology 16, no. 1 (January 1, 1988): 18–43. http://dx.doi.org/10.2346/1.2148795.
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Abstract Mathematical models of finite deformation of a rolling viscoelastic cylinder in contact with a rough foundation are developed in preparation for a general model for rolling tires. Variational principles and finite element models are derived. Numerical results are obtained for a variety of cases, including that of a pure elastic rubber cylinder, a viscoelastic cylinder, the development of standing waves, and frictional effects.
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Dembiczak, Tomasz, and Marcin Knapiński. "Shaping Microstructure and Mechanical Properties of High-Carbon Bainitic Steel in Hot-Rolling and Long-Term Low-Temperature Annealing." Materials 14, no. 2 (January 14, 2021): 384. http://dx.doi.org/10.3390/ma14020384.
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Based on the research results, coefficients in constitutive equations, describing the kinetics of dynamic, meta-dynamic, and static recrystallization in high-carbon bainitic steel during hot deformation were determined. The developed mathematical model takes into account the dependence of the changing kinetics in the structural size of the preliminary austenite grains, the value of strain, strain rate, temperature, and time. Physical simulations were carried out on rectangular specimens. Compression tests with a flat state of deformation were carried out using a Gleeble 3800. Based on dilatometric studies, coefficients were determined in constitutive equations, describing the grain growth of the austenite of high-carbon bainite steel under isothermal annealing conditions. The aim of the research was to verify the developed mathematical models in semi-industrial conditions during the hot-rolling process of high-carbon bainite steel. Analysis of the semi-industrial studies of the hot-rolling and long-term annealing process confirmed the correctness of the predicted mathematical models describing the microstructure evolution.
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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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Volkov, Ivan, Leonid Igumnov, and Denis Shishulin. "Evaluating long-term strength of structures." Thermal Science 23, Suppl. 2 (2019): 477–88. http://dx.doi.org/10.2298/tsci19s2477v.
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The issue of evaluating strength and service life is discussed as applied to structures, the exploitation properties of which are characterized by multi-parametric nonstationary thermal mechanical effects. The main requirements to mathematical models of the related processes are formulated. In the framework of mechanics of damaged media, a mathematical model describing processes of inelastic deformation and damage accumulation due to creep is developed. The mechanics of damaged media model consists of three interconnected parts: relations defining inelastic behavior of the material accounting for its dependence on the failure process, equations describing kinetics of damage accumulation, and a strength criterion of the damaged material. The results of numerically simulating the carrying capacity of a nuclear power plant reactor vessel in the event of a hypothetical emergency are presented. Emergency conditions were modeled by applying pressure modeling the effect of melt-down, the constant internal pressure and temperature varying within the part of the vessel in question. The analysis of the obtained numerical results made it possible to note a number of characteristic features accompanying the process of deformation and failure of such facilities, connected with the time and place of the forming macrocracks, the stressed-strained state history and the damage degree in the failure zone, etc. The results of comparing the numerical and experimental data make it possible to conclude that the proposed defining relations of mechanics of damaged media adequately describe degradation of the initial strength properties of the material for the long-term strength mechanism and can be effectively used in evaluating strength and service life of structures under thermal mechanical loading.
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Chereches, Tudor, Paul Lixandru, Sergiu Mazuru, Pavel Cosovschi, and Daniel Dragnea. "Numerical Simulation of Plastic Deformation Process of the Glass Mold Parts." Applied Mechanics and Materials 657 (October 2014): 126–31. http://dx.doi.org/10.4028/www.scientific.net/amm.657.126.
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In our present days numerical simulation became an important tool of engineering. Numerical simulation methods allow quantitative examination of the complex processes and phenomena in the general area of physics and also provide an insight in their dynamic evolution and even can become important tools for the discovery of new phenomena. In essence, the numerical simulation transfer important aspect of physical reality in discrete forms of mathematical description recreates and solves the problems on computer and finally, highlights issues that the analyst required. This modern numerical method approach, attacks the original problems in all their details on a much larger platform with a much smaller number of assumptions and approximations, in comparison to traditional methods. Transposition of the physics problems in the virtual space, governed by the force of computers, numerical simulation - as scientific approach - is becoming increasingly interesting for many fields of research. Basically, by means of numerical simulation are addressed fields such as mechanics deformable solids, fluid mechanics, aerodynamics, biomechanics, astrophysics. Numerical simulations follow a similar procedure to all the scientific approach, which consists in going through several stages, as follows: the phenomenon, the physical model, mathematical model, discrete model, and coding, numerical solution. In the plastic deformation of metals are involved, besides the mechanical properties and some thermal properties because even if the process is applied in the initial state to a cold material, along the process changes occur because of friction between materials and tools and transformation of plastic mechanical work into heat. Basic mechanical properties of the materials are underline through characteristic diagrams of materials obtained in simple tests of traction and compression. These tests were carried out in the Polytechnic University of Bucharest, Romanian Research & Development Institute for Gas Turbines COMOTI, Institute for Calculating and Testing Aero-Astronautic Structures STRAERO, SC UPS PILOT ARM Ltd, and Asachi Technical University of Iasi. To achieve the major objectives of the numerical simulation of the technological process of cold plastic deformation, are incorporated into the physical model three types of surfaces: cylindrical, conical and profiled. The sizes of the initial geometry were established in accordance with the basic dimensions of processed products by this method. For delimiting surfaces to be machined, the addition of grip (the tail) has a reduced diameter. Geometric models provide strength and rigidity needed for safely and accurately processing technology of cold plastic deformation. Geometric models and specimens which had been subjected to tensile tests, compression and hardness were made in the Glass Factory, Chisinau, Moldova.
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Ignatyuk, Roman, Oleksandr Ryzhyi, Leonid Serilko, Oleksandr Stadnyk, and Dmytro Serilko. "JUSTIFICATION OF TRANSPORT PARAMETERS AND MODELING OF THE PROCESS OF DESTRUCTION OF THE ELASTIC-PLASTIC ENVIRONMENT." Transactions of Kremenchuk Mykhailo Ostrohradskyi National University, no. 5(130) (October 27, 2021): 89–96. http://dx.doi.org/10.30929/1995-0519.2021.5.89-96.
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Purpose. The substantiation of the mathematical model of mechanical deformation of the elastic-plastic medium and the modeling of the transport process of the expansion assemblies. Methodology. Mathematical and theoretical studies were based on the fundamental theory of continuum mechanics and general positions of engineering mechanics. Analytical and graphical analysis of mathematical models carried out on a PC in a specialized software complex. Results. In the current conditions of economic development of the country, considerable attention should be paid to the development and modernization of certain sectors of the economy. Significant amounts of work, which are accompanied by the development of soil of different properties, which can be defined as an elastic-plastic material. These studies will solve a number of problems that are acute not only in agriculture but also in construction, in the open pit mining, reclamation, one of which is an imperfect process of loosening the soil during its cultivation. Therefore, the urgent problem is to establish rational parameters of the transport surface of the unit for loosening the elastic-plastic material. The developed mathematical model allows determining the emerging stress, which in turn determines the boundary of the destruction of the elastic-plastic material. In the design of lining assemblies, it is advisable to have a radius of the outlet section R = 0.18 m or more. Originality. The mathematical models for the process of destruction of elastic-plastic material and forecasting of optimal transport parameters for designing of expansion assemblies are obtained. Practical value. The developed mathematical model will provide an improvement in the process of loosening elastic-plastic material, and engineering calculations during the design of the rutter can prevent unwarranted increase in resistance, with displaced materials on the cutting surface. References 10, figures 8.
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Okamoto, R. J., M. J. Moulton, S. J. Peterson, D. Li, M. K. Pasque, and J. M. Guccione. "Epicardial Suction: A New Approach to Mechanical Testing of the Passive Ventricular Wall." Journal of Biomechanical Engineering 122, no. 5 (May 30, 2000): 479–87. http://dx.doi.org/10.1115/1.1289625.
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The lack of an appropriate three-dimensional constitutive relation for stress in passive ventricular myocardium currently limits the utility of existing mathematical models for experimental and clinical applications. Previous experiments used to estimate parameters in three-dimensional constitutive relations, such as biaxial testing of excised myocardial sheets or passive inflation of the isolated arrested heart, have not included significant transverse shear deformation or in-plane compression. Therefore, a new approach has been developed in which suction is applied locally to the ventricular epicardium to introduce a complex deformation in the region of interest, with transmural variations in the magnitude and sign of nearly all six strain components. The resulting deformation is measured throughout the region of interest using magnetic resonance tagging. A nonlinear, three-dimensional, finite element model is used to predict these measurements at several suction pressures. Parameters defining the material properties of this model are optimized by comparing the measured and predicted myocardial deformations. We used this technique to estimate material parameters of the intact passive canine left ventricular free wall using an exponential, transversely isotropic constitutive relation. We tested two possible models of the heart wall: first, that it was homogeneous myocardium, and second, that the myocardium was covered with a thin epicardium with different material properties. For both models, in agreement with previous studies, we found that myocardium was nonlinear and anisotropic with greater stiffness in the fiber direction. We obtained closer agreement to previously published strain data from passive filling when the ventricular wall was modeled as having a separate, isotropic epicardium. These results suggest that epicardium may play a significant role in passive ventricular mechanics. [S0148-0731(00)00305-8]
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Hsu, Tze-Chi, and William R. D. Wilson. "Refined Models for Hydrodynamic Lubrication in Axisymmetric Stretch Forming." Journal of Tribology 116, no. 1 (January 1, 1994): 101–9. http://dx.doi.org/10.1115/1.2927023.
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Two mathematical models for axisymmetric stretch forming with a spherical punch are developed. The models combine a finite element representation of the sheet deformation with a hydrodynamic lubrication model. In one model the influence of sheet bending stiffness is taken into account while in the other only the membrane stiffness is considered. Comparison of the predictions of the models with the film thickness measurements of Hector and Wilson indicates that the inclusion of elastic effects is important in predicting lubricant film thickness. The results of the bending model are in particularly good agreement with the experimental data. A useful analytical method for predicting the film thickness at the center of the conjunction at the onset of yield is also developed.
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Du, Fei, Peng Zhou, Peng Guo, Cheng Li, Lei Deng, Xinyun Wang, and Junsong Jin. "Effect of Hot Deformation Parameters on Heat-Treated Microstructures and Mechanical Properties of 300M Steel." Materials 15, no. 24 (December 14, 2022): 8927. http://dx.doi.org/10.3390/ma15248927.
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The high strength of 300M steel originates from the heat treatment process after forging, but how hot deformation affects the heat-treated microstructure and mechanical properties is unclear. In this study, compression tests under different hot deformation parameters and post-deformation heat treatment experiments were carried out, and the martensite transformation process was investigated using in situ observation. The results show that the grain size of the specimen deformed at low temperature and high strain rate is smaller, and annealing twins will be formed. Both austenite grain boundaries and twin boundaries hinder the growth of martensite blocks, reducing the size of martensite units after heat treatment and thus resulting in higher yield strength. Besides, the mathematical models were established to describe the relationship between hot deformation parameters and grain size after deformation, martensite packet size and martensite block width, respectively, after heat treatment. The relationship between yield strength and hot deformation parameters was also analyzed. According to the results and models, the hot deformation parameters would be optimized more reasonably to improve the final mechanical properties of 300M steel forgings.
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Wang, Hong, Xiao Shuang Men, Yu Xian Zhang, Fang Yao, and Li Fu Wang. "Mechanical Analysis of Machining Error in Turning Slender Shafts by Reversible Turning Technique." Advanced Materials Research 337 (September 2011): 430–33. http://dx.doi.org/10.4028/www.scientific.net/amr.337.430.
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Mechanical analysis is carried out to the deformation of workpiece when turning slender shafts in the normal and reversed direction under two different conditions of clamping. Mathematical models are set up for the calculation of bending deformation resulting from cutting force in condition of normal and reversed turning. An example is given to show that bending deformation and the resulting machining error in conditions of reversed turning is much less than that in normal turning. The result has been verified by experiments. The mechanical model and numerical analysis can be used in the processing design of slender shaft turning.
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Siciliano, Fulvio. "Mathematical Modelling of Hot Rolling: A Practical Tool to Improve Rolling Schedules and Steel Properties." Materials Science Forum 762 (July 2013): 210–17. http://dx.doi.org/10.4028/www.scientific.net/msf.762.210.
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Most of the commercial metallic materials undergo at least one hot deformation stage during fabrication. Hot deformation processing leads to the production of plates, strips, rods, pipes and other shapes at lower overall cost when compared to the cold deformation/annealing route. Comprehensive study of the metallurgical phenomena during hot deformation has enormous potential application in the control of industrial rolling processes. Understanding of the microstructural and mean flow stress evolution lead to sound steel developments and innovative rolling schedules. The models predict parameters such as grain size, fractional softening (static and dynamic) and strain induced precipitation which are useful to improve rolling schedules. Effects such as incomplete softening and strain accumulation can be easily detected as well as their consequences on the final grain size and mechanical properties. In this regard, special attention must be given to steels, the most important metallic material in terms of history, present and future. In this paper, three hot rolling routes will be analyzed in order to produce high strength linepipe steels. Examples were selected on how the use of modelling during development stage can help to meet mechanical properties, mainly toughness and drop weight tear test. Firstly, it is presented a brief overview on mathematical models applied to hot rolling. Thin slab casting/direct rolling, hot strip mill and plate mill are exemplified in the present work. The development of new steel grades can greatly accelerated with the aid of modelling, which is an useful, low-cost technique.
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Ajani, Ibrahim, and Cong Lu. "Assembly variation analysis of the non-rigid assembly with a deformation gradient model." Assembly Automation 42, no. 1 (November 18, 2021): 40–53. http://dx.doi.org/10.1108/aa-07-2021-0092.
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Purpose This paper aims to develop a mathematical method to analyze the assembly variation of the non-rigid assembly, considering the manufacturing variations and the deformation variations of the non-rigid parts during the assembly process. Design/methodology/approach First, this paper proposes a deformation gradient model, which represents the deformation variations during the assembly process by considering the forces and the self-weight of the non-rigid parts. Second, the developed deformation gradient models from the assembly process are integrated into the homogenous transformation matrix to model the deformation variations and manufacturing variations of the deformed non-rigid part. Finally, a mathematical model to analyze the assembly variation propagation is developed to predict the dimensional and geometrical variations due to the manufacturing variations and the deformation variations during the assembly process. Findings Through the case study with a crosshead non-rigid assembly, the results indicate that during the assembly process, the individual deformation values of the non-rigid parts are small. However, the cumulative deformation variations of all the non-rigid parts and the manufacturing variations present a target value (w) of −0.2837 mm as compared to a target value of −0.3995 mm when the assembly is assumed to be rigid. The difference in the target values indicates that the influence of the non-rigid part deformation variations during the assembly process on the mechanical assembly accuracy cannot be ignored. Originality/value In this paper, a deformation gradient model is proposed to obtain the deformation variations of non-rigid parts during the assembly process. The small deformation variation, which is often modeled using a finite-element method in the existing works, is modeled using the proposed deformation gradient model and integrated into the nominal dimensions. Using the deformation gradient models, the non-rigid part deformation variations can be computed and the accumulated deformation variation can be easily obtained. The assembly variation propagation model is developed to predict the accuracy of the non-rigid assembly by integrating the deformation gradient models into the homogeneous transformation matrix.
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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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Dmitriev, Vladimir G., Alexander N. Danilin, Anastasiya R. Popova, and Natalia V. Pshenichnova. "Numerical Analysis of Deformation Characteristics of Elastic Inhomogeneous Rotational Shells at Arbitrary Displacements and Rotation Angles." Computation 10, no. 10 (October 11, 2022): 184. http://dx.doi.org/10.3390/computation10100184.
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Adequate mathematical models and computational algorithms are developed in this study to investigate specific features of the deformation processes of elastic rotational shells at large displacements and arbitrary rotation angles of the normal line. A finite difference method (FDM) is used to discretize the original continuum problem in spatial variables, replacing the differential operators with a second-order finite difference approximation. The computational algorithm for solving the nonlinear boundary value problem is based on a quasi-dynamic form of the ascertainment method with the construction of an explicit two-layer time-difference scheme of second-order accuracy. The influence of physical and mechanical characteristics of isotropic and composite materials on the deformation features of elastic spherical shells under the action of surface loading of “tracking” type is investigated. The results of the studies conducted have shown that the physical and mechanical characteristics of isotropic and composite materials significantly affect the nature of the deformation of the clamped spherical shell in both the subcritical and post-critical domains. The developed mathematical models and computational algorithms can be applied in the future to study shells of rotation made of hyperelastic (non-linearly elastic) materials and soft shells.
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Tiernan, P., and M. T. Hillery. "Experimental and numerical analysis of the deformation in mild steel wire during dieless drawing." Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications 216, no. 3 (July 1, 2002): 167–78. http://dx.doi.org/10.1177/146442070221600302.
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Dieless wire drawing is the process of causing a reduction in a wire diameter without the use of conventional wire drawing dies. The wire, axially loaded with a force, is heated to an elevated temperature to initiate plastic deformation. The mechanics of this novel drawing process and a theoretical analysis of the deformation are discussed in this paper. The results of an experimental drawing programme carried out with mild steel wire at temperatures between 400 and 900°C are also presented. Mathematical models were developed and used to describe and predict the process deformation and both the stress and temperature distribution profile along the workpiece. A machine was designed and manufactured to facilitate an experimental programme of dieless drawing. The machine permitted continuous drawing of wire, while the reduction ratio, drawing load and temperature were automatically controlled using a personal computer. A finite element (FE) model of the wire was developed, and the results obtained from the FE analysis show good agreement with those obtained from both the experimental work and the mathematical modelling. Results obtained confirm that a complicated interdependence of the process parameters exists during the dieless drawing process.
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Jędrzejczyk, D., M. Hojny, and M. Głowacki. "Development of Software for the Simulation of Rolling Steel Under the Coexistence of Liquid and Solid State / Rozwój Oprogramowania Do Symulacji Walcowania Stali W Warunkach Współistnienia Fazy Ciekłej I Stałej." Archives of Metallurgy and Materials 60, no. 4 (December 1, 2015): 2783–90. http://dx.doi.org/10.1515/amm-2015-0447.
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The paper presents the results of the application simulating the rolling process of steel in terms of coexistence of liquid and solid phases. The created mathematical models can be the basis for creation of systems that simulate the final phase of the continuous casting process relying on using a roller burnishing machine for continuous casting of steel. For a complete description of the performance of the material during deformation in these conditions, the constructed mathematical model is a fully three-dimensional model and consists of three parts: thermal, mechanical, and density variation submodels. The thermal model allows the prediction of temperature changes during plastic deformation of solidifying material. The mechanical model determines the kinetics of plastic continuum flow in the solid and semi-solid states, and the resulting deformation field. The temperature of the process forces supplementing the description of the performance of the material with a density variation model that allows the prediction of changes in the density of the material during the final phase of solidification with simultaneous plastic deformation. For the purpose built model, experimental studies were performed using a physical simulator Gleeble 3800®. They allowed the determination of the necessary physical properties of the metal within the temperature of change state. In addition to presenting the developed models the work also includes the description of the author’s application that uses the above mathematical models. The application was written in the fully object-oriented language C++ and is based on the finite element method. The developed application beside the module data input, also consist of a module of three-dimensional visualization of the calculations results. Thanks to it, the analysis of the distribution of the particular rolling parameters in any cross-section of the rolled strip will be possible. The paper presents the results of the authors’ research in the area of the advanced computer simulation.
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Li, Xin, Zhengdong Lei, Qinghui Zhang, and Yuanqing Zhang. "A Geocoupling Simulation Method for Fractured Reservoir Production." Geofluids 2022 (September 23, 2022): 1–13. http://dx.doi.org/10.1155/2022/1293143.
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Reservoir simulation is critical to the design of reservoir development plan and has been extensively used. However, it is challengeable for to simulate the production process for fractured reservoirs, because of the fracture geometry and the fracture deformation. Specifically, three problems need to be solved. First, there is a lack of mathematical models that can predict the fracture deformation with acceptable precision. Second, the fracture deformation is stress-dependent; therefore, a geocoupled equation should be used to quantify the stress change, but the solution is extremely expensive. Third, the fracture geometries pose great challenges to traditional gridding techniques. This paper proposes a new geocoupling simulation method that is capable of modeling the complex fracture geometry as well as the fracture mechanical behavior. The geomechanical effects and the reservoir production performance are modeled through an implicit geocoupled model, which is developed based on the poro-mechanics theory. The fixed stress strategy is used to solve the geocoupled equations. Moreover, a comprehensive fracture modeling method is proposed, in terms of the fracture deformation model and the fracture gridding technique to model the fracture effects. Ultimately, this method is used to analyze two field-scale cases. The results demonstrate that this method exhibits good practicability and has practical significance for fractured reservoir development.
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Masuda, Hiroshi. "Feature-preserving Deformation for Assembly Models." Computer-Aided Design and Applications 4, no. 1-4 (January 2007): 311–20. http://dx.doi.org/10.1080/16864360.2007.10738551.
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Masuda, Hiroshi, and Kenta Ogawa. "Interactive Deformation of 3D Mesh Models." Computer-Aided Design and Applications 5, no. 1-4 (January 2008): 47–57. http://dx.doi.org/10.3722/cadaps.2008.47-57.
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Consuegra, Franklin, Antonio Bula, Wilson Guillín, Jonathan Sánchez, and Jorge Duarte Forero. "Instantaneous in-Cylinder Volume Considering Deformation and Clearance due to Lubricating Film in Reciprocating Internal Combustion Engines." Energies 12, no. 8 (April 15, 2019): 1437. http://dx.doi.org/10.3390/en12081437.
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A new methodology for predicting the real instantaneous in-cylinder volume in the combustion chamber of a reciprocating internal combustion engine is implemented. The mathematical model developed as part of this methodology, takes into consideration the deformations due to pressure and inertial forces, via a deformation constant adjusted through ANSYS®, using a high-precision CAD model of a SOKAN SK-MDF300 engine. The deformation constant was obtained from the CAD model using the computational tool ANSYS® and the pressure data was obtained from the engine running at three regimes: 1500, 2500, and 3500 rpm. The results were compared with previous models reported in the literature, showing that the deformation constant obtained has a smaller variation among cycles, which leads to a more precise value of the mechanical deformations. Furthermore, to have a more accurate model of the instantaneous volume variation, a factor taking into consideration the lubricant film behavior is introduced to calculate volumetric variation due to geometrical clearances. The influence of the introduced volumetric variation was evaluated through a process of combustion diagnosis, evidencing the improvement in the predictive capacity of thermodynamic modeling and, therefore, the correct prediction of heat release rate.
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Han, Rui, and Jinju Chen. "A modified Sneddon model for the contact between conical indenters and spherical samples." Journal of Materials Research 36, no. 8 (April 28, 2021): 1762–71. http://dx.doi.org/10.1557/s43578-021-00206-5.
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AbstractIndentation techniques have proven to be effective to characterize the mechanical properties of materials. For the elastic deformation, the commonly used models are Hertz model and Sneddon model. However, neither of them works for indenting the spherical samples using the pyramid or conical indenter. Therefore, one modified Sneddon model has been developed to determine the Young’s modulus of spherical samples from indentation results. In this study, the effects of sample diameter and indenter angles on indentation tests were investigated by finite element method (FEM). The empirical correction parameters in the new mathematical model were introduced based on dimensional analysis and determined by the numerical fitting to FEM results. Experimental tests with different conical indenters have demonstrated that the new model is capable to reliably determine the Young’s modulus of the spherical samples. The new model can fill the gap of the contact mechanics and enrich the experimental solid mechanics for the interpretation of indentation results. Graphic abstract
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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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Kaminska, Marianna, Valerii Degtuar, and Oleksandr Yaresko. "Mathematical modeling of the chest, its funnel-shaped deformation and thoracoplasty." ORTHOPAEDICS, TRAUMATOLOGY and PROSTHETICS, no. 2 (October 12, 2021): 17–22. http://dx.doi.org/10.15674/0030-59872021217-22.
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The most common method of treating of the congenital funnel-shaped chest is thoracoplasty method by D. Nuss. During this surgery, a significant mechanical effect is created on the ribs, sternum, spinal column, which act instantly and continuously for a long time and create new biomechanical conditions for the «chest – rib – spine» system. Objective. To construct a functional model of the chest with a spinal column, which takes into account the movements in the costal-vertebral joints, it allows modeling the funnel-shaped deformation in conditions close to the reality, its operative correction, predicting the results and choosing the optimal parameters of thoracoplasty. Methods. Normal and funnel-shaped chest models based on the articular connection of the ribs to the spine were created using SolidWorks. The main calculations were made using the ANSYS program. To estimate the stress-strain state (SSS), stresses are selected by Mises. Results. The created dynamic mathematical model of the chest makes it possible to conduct a reliable analysis of the biomechanical interaction of the plate with the chest, to analyze the stress-strain state of the constructed models in the norm, with and without taking into account the movements in the costal-vertebral joints. In addition, it allows to simulate the operation by D. Nuss and to study the biomechanical changes in conditions close to reality, occurring in the «chest – rib – spine» system, to determine the areas of maximum loads and safety boundaries. Conclusions. The reproduction of articular ribs rotation in the dynamic model changes the picture of the SSS distribution. In the case of modeling the correction of funnel-shaped deformation of the chest by the method by D. Nuss, the largest zone of stress concentration was found on the outer posterior surface of the sixth pair of ribs. The most tense vertebrae were ThV– ThVI, but the maximum values did not exceed the permissible values. In the case of a lower plate conduction, the correction is achieved with better SSS values in the higher elements of the «chest – ribs – spine» system.
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Wijata, Adam, Jan Awrejcewicz, Jan Matej, and Michał Makowski. "Mathematical model for two-dimensional dry friction modified by dither." Mathematics and Mechanics of Solids 22, no. 10 (June 2, 2016): 1936–49. http://dx.doi.org/10.1177/1081286516650483.
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A new dynamic two-dimensional friction model is developed that is based on the bristle theory. Actually, it is the Reset Integrator Model converted into a two-dimensional space. Usually, two-dimensional friction models are in fact one-dimensional models that are rotated into a slip velocity direction. However, this common approach cannot be applied to the bristle model. That is why the idea of a two-dimensional bristle is presented. The bristle’s deformation is described using polar coordinates. The carried-out numerical simulation of a planar oscillator has proved that the new model correctly captures the mechanism of smoothing dry friction by dither applied in both a perpendicular and co-linear way regarding body velocity. Furthermore, the introduced mathematical model captures two-dimensional stick-slip behaviour. Cartesian slip velocity components are the only inputs to the model. In addition, our proposed model allows one to describe friction anisotropy using bristle parameters. The paper contains the results of an experimental verification of the new friction model, conducted with a special laboratory rig employed to investigate a two-dimensional motion in the presence of dither as well as to validate our numerical results.
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Sanzharovsky, Rudolf S., Maxim M. Manchenko, Muhlis A. Hadzhiev, Turlybek T. Musabaev, Tatyana N. Ter-Emmanuilyan, and Kirill A. Varenik. "System of insufficiency of the modern theory of long-term resistance of reinforced concrete and designers’ warnings." Structural Mechanics of Engineering Constructions and Buildings 15, no. 1 (December 15, 2019): 3–24. http://dx.doi.org/10.22363/1815-5235-2019-15-1-3-24.
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Aim of the research. The essence of the failure of the globally widespread theory of long-term resistance of reinforced concrete is defined and analyzed. Methods. This failure includes the following interconnected parts: 1) the set of ten basic fundamental properties of structural concrete is completely distorted (for example, instantaneous linear properties are Maxwell scheme); 2) mathematical rules are violated when recording the rates of elastic deformation and creep deformation, due to a misunderstanding of the Boltzmann principle (these violations distort the whole structure of the theory); 3) the rules of classical mechanics are violated, what is caused by substitution of fundamental properties of concrete with various “chain models” (for example, the principle of independence of action of forces, which is the fourth fundamental law of Galileo - Newton, is violated); 4) sections of the general “world theory of creep of reinforced concrete”, based on its algebraization, in their essence reject the fundamental law of natural science - Newton's second law: not only the inertial component is rejected, but also forces depending on speed (in this way the “world theory of creep of reinforced concrete” is degraded to the level of Aristotle’s mechanics); 5) unacceptably idealized creep theories and structural models that endow concrete with unrealizable properties, especially flagrant in zones of cracks, are incorporated in the normative calculations of structures; 6) solid design companies of the world show that concrete creep is not a scientific theory: this is a warning to designers. Results. The performed analysis is accompanied by necessary mathematical calculations and experimental estimates.
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Kislitsyn, V. D., K. A. Mokhireva, V. V. Shadrin, and A. L. Svistkov. "Research and Modeling of Viscoelastic Behavior of Elastomeric Nanocomposites." PNRPU Mechanics Bulletin, no. 2 (December 15, 2021): 76–87. http://dx.doi.org/10.15593/perm.mech/2021.2.08.
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The paper presents results of studying mechanical properties of polymer composites depending on types of filler particles (granular - carbon black, nanodiamonds; layered - graphene plates; fibrous - single-walled nanotubes). These nanofillers differ greatly from each other in their structure and geometry. A significant difference in behavior of nanocomposites was revealed even with little introduction of particles into the elastomer. The highest level of reinforcement of the matrix was obtained when single-wall nanotubes and detonation nanodiamonds were used as fillers. The viscoelastic properties and the Mullins softening effect [1-4] were investigated in experiments performed with material samples subjected to complex uniaxial cyclic deformation. In these experiments, the amplitude of deformations was changed step by step; and at each step a time delay was specified to complete rearrangement processes of the material structure. It was found that a pronounced softening effect after the first cycle of deformation and significant hysteresis losses occur in the material filled with single-walled nanotubes. These characteristics are insignificant for the rest of nanocomposites until elongation increases twofold. In accordance with the obtained results, a new version of the mathematical model to describe properties of the viscoelastic polymer materials was proposed. The constants of the constitutive relations were calculated for each material; the theoretical and experimental load curves were compared. As a result, the introduced model is able to describe the behavior of elastomeric nanocomposites with a high accuracy. Moreover, this model is relatively easy to use, suitable for a wide range of strain rates and stretch ratios and does not require the entire history of deformation as needed for integral models of viscoelasticity.
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Dymova, L. G., P. V. Sevast'yanov, and V. I. Timoshpol'skii. "Comparative analysis of mathematical models for thermal stress and deformation generation in a solidifying ingot." Journal of Engineering Physics 60, no. 1 (January 1991): 99–104. http://dx.doi.org/10.1007/bf00871621.
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Yue, Feng, Ziyan Wu, Zhiqiang Fan, and Haokai Li. "Two Novel Vlasov Models for Bending Analysis of Finite-Length Beams Embedded in Elastic Foundations." Buildings 12, no. 8 (July 29, 2022): 1122. http://dx.doi.org/10.3390/buildings12081122.
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The issue of soil–structure interaction (SSI) is essentially to analyze the influence of complex media on the mechanical behavior of supported structures. With the development of underground space, geological structures and space constraints put forward higher requirements for foundations and buildings. In this paper, the effects of soil heterogeneity and embedment depth on the bending of finite-length beams embedded in two novel Vlasov elastic foundations are investigated. Firstly, the constitutive relations of subsoil are simulated by Gibson and transversely isotropic soils, and the type of elastic foundation is described by the modified Vlasov model. Then, based on variational principles, the governing differential equations for the deformation and attenuation parameters of beams embedded in elastic foundations are derived by taking the variation of the minimum potential energy of the system, and the characteristic coefficient related to the embedment depth is introduced. Finally, the mechanical performance of the beam and foundation is obtained by an iterative technique and the Fourier series method, and an extensive parametric study is performed to examine influence of some basic parameters on the deformation and internal forces of the system. The results show that the mathematical expressions of two refined elastic models are in good agreement with those of the traditional Vlasov foundation after degradation. The iterative technique based on the principles of solid mechanics can be employed to obtain more reliable model parameters. More importantly, with the increase in the embedment depth, the mechanical responses of the beam and subgrade forces decrease. The main reason is that the restraint effect of the soil media around structures, which leads to the reduction of the characteristic coefficient affecting the displacement of beams. Moreover, the heterogeneity of soil, including Gibson characteristics and transverse isotropy, should be considered according to specific working conditions in civil engineering.
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Man, Xiaolin, and Colby C. Swan. "A Mathematical Modeling Framework for Analysis of Functional Clothing." Journal of Engineered Fibers and Fabrics 2, no. 3 (September 2007): 155892500700200. http://dx.doi.org/10.1177/155892500700200302.
Full textAbstract:
In the analysis and design of functional clothing systems, it is helpful to quantify the effects of a system on a wearer's physical performance capabilities. Toward this end, a clothing modeling framework for quantifying the mechanical interactions between a given clothing system design and a specific wearer performing defined physical tasks is proposed. The modeling framework consists of three interacting modules: (1) a macroscale fabric mechanics/dynamics model; (2) a collision detection and contact correction module; and (3) a human motion module. In the proposed framework, the macroscopic fabric model is based on a rigorous large deformation continuum-degenerated shell theory representation. Material models that capture the stress-strain behavior of different clothing fabrics are used in the continuum shell framework. The collision and contact module enforces the impenetrability constraint between the fabric and human body and computes the associated contact forces between the two. The human body is represented in the current framework as an assemblage of overlapping ellipsoids that undergo rigid body motions consistent with human motions while performing actions such as walking, running, or jumping. The transient rigid body motions of each ellipsoidal body segment in time are determined using motion capture technology. The integrated modeling framework is then exercised to quantify the resistance that the clothing exerts on the wearer during the specific activities under consideration. Current results from the framework are presented and its intended applications are discussed along with some of the key challenges remaining in clothing system modeling.
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Fan, Bai Lin, Ke Zhi Guan, and Gang Han Huang. "Research on Flow Stress for 00Cr12Ti Stainless Steel." Advanced Materials Research 199-200 (February 2011): 1945–48. http://dx.doi.org/10.4028/www.scientific.net/amr.199-200.1945.
Full textAbstract:
Flow stress of hot deformation about 00Cr12Ti stainless steel was experimentally studied by A Gleeble1500 thermo-mechanical simulator. The effects of deformed temperature, strain rate and strain to flow stress were analyzed .multiple Non-linear regression mathematical models of flow stress were proposed. 00Cr12Ti flow stress varies with temperature more slowly through 00Cr12Ti compared with 0Cr13Mn.