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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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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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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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Ivanov, Evgeny, Olaf Lechtenfeld, and Stepan Sidorov. "Deformed N = 8 Supersymmetric Mechanics." Symmetry 11, no. 2 (January 26, 2019): 135. http://dx.doi.org/10.3390/sym11020135.
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We give a brief review of deformed N = 8 supersymmetric mechanics as a generalization of SU(2|1) mechanics. It is based on the worldline realizations of the supergroups SU(2|2) and SU(4|1) in the appropriate N = 8 , d = 1 superspaces. The corresponding models are deformations of the standard N = 8 mechanics models by a mass parameter m.
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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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Moerman, Kevin M., Behrooz Fereidoonnezhad, and J. Patrick McGarry. "Novel hyperelastic models for large volumetric deformations." International Journal of Solids and Structures 193-194 (June 2020): 474–91. http://dx.doi.org/10.1016/j.ijsolstr.2020.01.019.
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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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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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Bulucea, Cornelia A., Constantin Brindusa, Doru A. Nicola, Nikos E. Mastorakis, Carmen A. Bulucea, and Philippe Dondon. "Evaluating through mathematical modelling the power equipment busbars electrodynamic strength under sudden short-circuit conditions." MATEC Web of Conferences 210 (2018): 02004. http://dx.doi.org/10.1051/matecconf/201821002004.
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The electrodynamic strength, as forces acting between the current-carrying electric circuits are exerted as long as the currents exist, and have the tendency of deformation and displacement of the circuits. In short-circuit regimes the strength in electrical equipment becomes severe. For instance, short-circuits highly affect power transformers connected to power transmission lines. The effects are also strong because of mechanical deformations occurring in the power transformer connection part. In line with this idea, in this paper it is made an analytical study upon the a.c. single-phase and a.c. three-phase electric circuits, taking into account the current instantaneous maximum value. The paper also entails numerical simulations of electrodynamic strength in power transformer busbars under short-circuit conditions. MATLAB software, with its specific extensions, enable simulation models to generate the charts of the electrodynamic forces in the power transformer connection bars.
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Clifton, R. J., and F. P. Chiang. "Experimental Mechanics." Applied Mechanics Reviews 38, no. 10 (October 1, 1985): 1279–81. http://dx.doi.org/10.1115/1.3143691.
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Mechanical failure of machine parts, structures, and microelectronic components has a strong negative impact on the safety, security, and productivity of our people. Prevention of these failures is a principal focus of solid mechanics, which uses analysis, experiment, and computation to provide the understanding necessary for failure reduction through improved design, fabrication, and inspection. Experimental mechanics plays a critical role in this effort since it provides the data base for the calculations and the means for testing the validity of proposed theoretical models of failure. Current trends in experimental mechanics show increased use of optical methods for monitoring the displacements, velocities, and strains of surfaces. This trend has gained impetus from the attractiveness of noncontact methods for hostile environments and dynamically loaded bodies. Advances in laser technology have enhanced the instrumentation associated with these methods. Another trend is the investigation of material behavior under more complex loading conditions, made possible by the availability of servo-controlled testing machines with computer interfaces. Still another trend is the increased attention given to defects, such as inclusions, cracks, and holes, because of their importance in failure mechanisms. Opportunities for future contributions from experimental mechanics appear to be great and to occur across a broad range of technological problems. A central theme of future research appears to be increased emphasis on measurements at the micron and submicron scale in order to advance the understanding of material response and failure at the micromechanical level. Increased attention will also be given to internal measurements of defects, deformations and residual stresses because of their importance in developing a fundamental understanding of failure. Automated data reduction and control of experiments will greatly increase the information obtained from experiments and its usefulness for the development of mathematical models. Other important research directions include improved methods for measurements of in situ stresses in rocks, improved measurements of displacements and physiological parameters in biological systems, capability for long-term monitoring of the integrity of structures, and improved sensors for feedback control of mechanical systems.
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Zhao, S. Z., X. Y. Xu, and M. W. Collins. "The numerical analysis of fluid-solid interactions for blood flow in arterial structures Part 1: A review of models for arterial wall behaviour." Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine 212, no. 4 (April 1, 1998): 229–40. http://dx.doi.org/10.1243/0954411981534015.
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The structural response of a large artery is characteristically complex and includes the highly non-linear, history-dependent response of a nonhomogeneous anisotropic structure undergoing finite deformations. The mechanics of the arterial wall has been studied for nearly two centuries. The goals of such research range from the desire to have a basic knowledge and understanding of the mechanics and physiology of this complex structure to the need for data and methods for the design of arterial prostheses. In this paper, the models for arterial wall behaviour are critically reviewed. Firstly, the structure and general characteristics of the arterial wall are discussed. This is followed by a comprehensive review of the constitutive laws. Finally, structural analyses of the arterial wall by mathematical and numerical methods are discussed. Predictions using the authors' preferred models give focus to important issues, and in Part 2 the review and predictions are extended to the fluid-solid coupled situation.
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Vorobyov, V. S., E. L. Karelina, O. A. Bender, and K. V. Katalymova. "STATISTICAL MODELS OF PHYSIC-MECHANICAL CHARACTERISTICS OF ROADS IN THE AREA OF CULVERTS." Vestnik SibADI 15, no. 4 (September 12, 2018): 560–73. http://dx.doi.org/10.26518/2071-7296-2018-4-560-573.
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Introduction. Increased technical requirements for roads, associated with increasing axial loads, the intensity and speed of vehicles, with the actual technical condition of the roads number, engineering structures, including culverts, activation of federal and regional services to bring the parameters of road surfaces to the world standards, all listed parameters pose the task in developing the mathematical modeling methods of physical-mechanical characteristics of soils in the culverts area. Therefore, such methods allow to reduce economic costs and time for carrying out experimental research of deformations based on the monitoring results of the soil roadbed and pavement.Materials and methods. The order of technical condition of the culverts’ research, pavement and physico-mechanical characteristics of soils, methods of experimental research were discussed in the article. Moreover, the approach to carrying out experimental works on penetration of pits in places of deformations and nearby was approved. Additionally, the evaluation of the soils condition on the roadbed and the annular space of the culverts was made.Results. The schemes of deformation and elasticity, density, humidity, consistency, plasticity number, fluidity, and physical properties of the soil are determined. The engineering-geological elements, mean values of density, humidity and compaction factor are established according to the research aim. Consequently, the values of the strain modules and the modulus of elasticity are calculated on the basis of compression and stamp tests.Discussion and conclusions. The dependence of the pavement on the physic-mechanical characteristics of the soil of the roadbed is proved. The correlation-regression analysis of soil characteristics is performed on the basis of experimental research. As a result, the regression equations are obtained in the annular space of culverts and at the distance of ± 30 m nearby. As could be proved, there are irregularities in the coverage of road clothes caused by drawdown in barrier locations. The physic-mechanical characteristics of the ground and strength characteristics are increased by culverts’ transfer on distance. The application of physic-mechanical characteristics of the soil together with experimental studies makes it possible to reduce labor costs, time and cost of testing.
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Guzev, Mikhail, and Vladimir Makarov. "Principles of the non-Euclidian model application to the problem of dissipative mesocracking structures of highly compressed rock and massifs modelling." E3S Web of Conferences 56 (2018): 02001. http://dx.doi.org/10.1051/e3sconf/20185602001.
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New experimental results such as “zonal disintegration” around deep openings and “reversible deformations” of highly compressed rock samples cannot be described correctly from contemporary rock mechanics, which is based on the principals of classical Continuum Mechanics theory. A new approach to rock mechanics mathematical models consists of the application of non-Euclidian modelling to the problem of the description of anomalous experimental results. This leads to the formation of the “Geomechanics of Highly Compressed Rock and Rock Massifs” - a new branch of the existing theory of Geomechanics - in which framework a radical rise in geodynamical phenomena forecasting can be achieved. Principles of the geomechanics of highly compressed rock and rock massifs are discussed in this paper. The effectiveness of the application of non-Euclidian modelling to the anomalous experimental effects observed in research is demonstrated on two hierarchical geomedia block levels such as rock samples and rock massif around underground openings.
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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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Hvozd, Viktor, Eugene Tishchenko, Andriy Berezovskyi, and Stanislav Sidnei. "Research of Fire Resistance of Elements of Steel Frames of Industrial Buildings." Materials Science Forum 1038 (July 13, 2021): 506–13. http://dx.doi.org/10.4028/www.scientific.net/msf.1038.506.
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The article considers and analyses the methods by which it is possible to carry out research to determine the fire resistance of elements of steel frames of industrial buildings. It is determined that it is expedient to use the means of computational fluid dynamics, which has no limitations due to the high cost, complexity, environmental friendliness and complexity in comparison with real experiments. In order to conduct the most reliable computational experiments, mathematical models of temperature and mechanical reaction to the thermal effect of fire were created, taking into account the equations of thermal conductivity, systems of differential equations of stress-strain state of solids in their numerical implementation based on the finite element method. The solution of mathematical models was carried out using computational fluid dynamics, which describes the process of heat and mass transfer in test fire furnaces during the determination of fire resistance of steel structures. According to the results of computational experiments it is shown that the limiting state of loss of bearing capacity of vertical and horizontal structures occurs due to the formation of a zone of plastic deformations taking into account the associative theory of plasticity. According to the results of computational experiments, the dependence of the limit of fire resistance on the level of applied load to structures, which is close to linear, was revealed. Based on the obtained dependences and the corresponding graphs, a technique is developed based on the use of maximum deformations of the elements with the corresponding fixation of the limit state on the loss of fire resistance in terms of bearing capacity by bending this curve.
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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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Krzysztof, Chelmiski. "On Noncoercive Models in the Theory of Inelastic Deformations with Internal Variables." ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 81, S3 (2001): 595–96. http://dx.doi.org/10.1002/zamm.20010811575.
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Dubko, A. G., R. S. Osipov, Yu V. Bondarenko, and O. F. Bondarenko. "Electronic devices for studying mechanical properties of biological tissues." Технология и конструирование в электронной аппаратуре, no. 5-6 (2020): 40–47. http://dx.doi.org/10.15222/tkea2020.5-6.40.
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The paper shows the relevance of studying the mechanical properties of biological tissues and biocompatible materials for solving the problems of general and reconstructive surgery, transplantology, manual therapy, virtual simulation of surgical operations, robotic surgery, etc. The authors present basic information about biological tissue as an object of research and give a brief overview of the devices used for studying the mechanical characteristics of biological tissues. An experimental system for testing deformations of biological tissues and biocompatible materials during compression is described. The system is developed using modern hardware and software, as well as effective technical solutions. The results of the practical use of the developed device are presented and the obtained dependences of the mechanical stress of biological tissue samples on their deformation under pressure are analyzed. The system has high metrological characteristics and low cost, and allows performing all the necessary functions for measuring, processing and visualizing the data. The measurements obtained with this system can help form the recommendations for doctors on choosing the optimal operation mode of medical devices and instruments in each specific case. In addition, the measured data can be used to create mathematical models of biological tissues and biocompatible materials in order to further carry out virtual experiments. In further studies, the authors plan to create the mathematical models of biological tissues based on the finite element method and using the actual values characterizing the tissue, obtained with the developed system.
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Eremeyev, Victor A., Faris Saeed Alzahrani, Antonio Cazzani, Francesco dell’Isola, Tasawar Hayat, Emilio Turco, and Violetta Konopińska-Zmysłowska. "On existence and uniqueness of weak solutions for linear pantographic beam lattices models." Continuum Mechanics and Thermodynamics 31, no. 6 (September 13, 2019): 1843–61. http://dx.doi.org/10.1007/s00161-019-00826-7.
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Abstract In this paper, we discuss well-posedness of the boundary-value problems arising in some “gradient-incomplete” strain-gradient elasticity models, which appear in the study of homogenized models for a large class of metamaterials whose microstructures can be regarded as beam lattices constrained with internal pivots. We use the attribute “gradient-incomplete” strain-gradient elasticity for a model in which the considered strain energy density depends on displacements and only on some specific partial derivatives among those constituting displacements first and second gradients. So, unlike to the models of strain-gradient elasticity considered up-to-now, the strain energy density which we consider here is in a sense degenerated, since it does not contain the full set of second derivatives of the displacement field. Such mathematical problem was motivated by a recently introduced new class of metamaterials (whose microstructure is constituted by the so-called pantographic beam lattices) and by woven fabrics. Indeed, as from the physical point of view such materials are strongly anisotropic, it is not surprising that the mathematical models to be introduced must reflect such property also by considering an expression for deformation energy involving only some among the higher partial derivatives of displacement fields. As a consequence, the differential operators considered here, in the framework of introduced models, are neither elliptic nor strong elliptic as, in general, they belong to the class so-called hypoelliptic operators. Following (Eremeyev et al. in J Elast 132:175–196, 2018. 10.1007/s10659-017-9660-3) we present well-posedness results in the case of the boundary-value problems for small (linearized) spatial deformations of pantographic sheets, i.e., 2D continua, when deforming in 3D space. In order to prove the existence and uniqueness of weak solutions, we introduce a class of subsets of anisotropic Sobolev’s space defined as the energy space E relative to specifically assigned boundary conditions. As introduced by Sergey M. Nikolskii, an anisotropic Sobolev space consists of functions having different differential properties in different coordinate directions.
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Shen, Li-Jun. "Fractional derivative models for viscoelastic materials at finite deformations." International Journal of Solids and Structures 190 (May 2020): 226–37. http://dx.doi.org/10.1016/j.ijsolstr.2019.10.025.
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Paggi, M., S. Kajari-Schröder, and U. Eitner. "Thermomechanical deformations in photovoltaic laminates." Journal of Strain Analysis for Engineering Design 46, no. 8 (September 13, 2011): 772–82. http://dx.doi.org/10.1177/0309324711421722.
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Recent experimental results based on the digital image correlation technique (U. Eitner, M. Köntges, R. Brendel, Solar Energy Mater. Solar Cells, 2010, 94, 1346–1351) show that the gap between solar cells embedded into a standard photovoltaic laminate varies with temperature. The variation of this gap is an important quantity to assess the integrity of the electric connection between solar cells when exposed to service conditions. In this paper, the thermo-elastic deformations in photovoltaic laminates are analytically investigated by developing different approximate models based on the multilayered beam theory. It is found that the temperature-dependent thermo-elastic properties of the encapsulating polymer layer are responsible for the deviation from linearity experimentally observed in the diagram relating the gap variation to the temperature. The contribution of the different material constituents to the homogenized elastic modulus and thermal expansion coefficient of the composite system is also properly quantified through the definition of weight factors of practical engineering use.
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Bdeiwi, Houda, Andrea Ciarella, Andrew Peace, and Marco Hahn. "Model structure effect on static aeroelastic deformation of the NASA CRM." International Journal of Numerical Methods for Heat & Fluid Flow 30, no. 9 (January 18, 2019): 4167–83. http://dx.doi.org/10.1108/hff-07-2018-0352.
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Purpose This paper aims to present a computational aeroelastic capability based on a fluid–structure interaction (FSI) methodology and validate it using the NASA Common Research Model (CRM). Focus is placed on the effect of the wind tunnel model structural features on the static aeroelastic deformations. Design/methodology/approach The FSI methodology couples high-fidelity computational fluid dynamics to a simplified beam representation of the finite element model. Beam models of the detailed CRM wind tunnel model and a simplified CRM model are generated. The correlation between the numerical simulations and wind tunnel data for varying angles of attack is analysed and the influence of the model structure on the static aeroelastic deformation and aerodynamics is studied. Findings The FSI results follow closely the general trend of the experimental data, showing the importance of considering structural model deformations in the aerodynamic simulations. A thorough examination of the results reveals that it is not unequivocal that the fine details of the structural model are important in the aeroelastic predictions. Research limitations/implications The influence of some changes in structural deformation on transonic wing aerodynamics appears to be complex and non-linear in nature and should be subject to further investigations. Originality/value It is shown that the use of a beam model in the FSI approach provides a reliable alternative to the more costly coupling with the full FE model. It also highlights the non-necessity to develop precise, detailed structural models for accurate FSI simulations.
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Choksi, R., G. Del Piero, I. Fonseca, and D. Owen. "Structured Deformations as Energy Minimizers in Models of Fracture and Hysteresis." Mathematics and Mechanics of Solids 4, no. 3 (September 1999): 321–56. http://dx.doi.org/10.1177/108128659900400304.
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Deng, Wubing, and Igor B. Morozov. "Mechanical interpretation and generalization of the Cole-Cole model in viscoelasticity." GEOPHYSICS 83, no. 6 (November 1, 2018): MR345—MR352. http://dx.doi.org/10.1190/geo2017-0821.1.
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The mechanical basis of the popular Cole-Cole rheological model in viscoelasticity is investigated by using Lagrangian mechanics with nonlinear energy dissipation. The Cole-Cole model is usually viewed as a convenient way to fit the observed frequency-dependent attenuation and velocity-dispersion spectra, but its time-domain and numerical formulations are complex and contradict standard physical principles. For example, time-domain modeling of Cole-Cole media requires special mathematical tools such as fractional derivatives, convolutional integrals, and/or memory variables. Nevertheless, we find that Cole-Cole spectra naturally arise from conventional mechanics with nonlinear internal friction (non-Newtonian viscosity). The Lagrangian mechanical formulation is applied to a finite body (a rock sample in a laboratory experiment) and a wave-propagating medium, in both cases providing rigorous differential equations of motion and revealing the time- and frequency-independent material properties. The model also leads to a generalized Cole-Cole (GCC) model with multiple internal variables (relaxation mechanisms), similar to the generalized standard linear solid (GSLS). As a practical application, the GSLS and GCC models are compared on interpretations of recent P-wave attenuation and dispersion measurements on bitumen-sand samples in the laboratory. The GSLS and GCC models can be used to predict the observed strain/stress ratios with adequate accuracy. However, each of these models offers certain advantages, which are the linearity (for GSLS) and potentially smaller number of dynamic variables and broader peaks in attenuation spectra (for GCC). Therefore, additional experiments focusing on linearity of internal friction are required to establish which of these models may be preferable for rock. The Lagrangian approach provides a simple and physically meaningful way for comparing all types of observations, formulating numerical modeling schemes, and predicting the propagation of waves and behavior of other deformations of earth media.
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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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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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Spagnuolo, Mario, and Ugo Andreaus. "A targeted review on large deformations of planar elastic beams: extensibility, distributed loads, buckling and post-buckling." Mathematics and Mechanics of Solids 24, no. 1 (February 5, 2018): 258–80. http://dx.doi.org/10.1177/1081286517737000.
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In this paper, we give a targeted review of the state of the art in the study of planar elastic beams in large deformations, also in the presence of geometric nonlinearities. The main scope of this work is to present the different methods of analysis available for describing the possible equilibrium forms and the motions of elastic beams. For the sake of completeness, we start by giving an overview of the nonlinear theories introduced for approaching this argument and then we account for the variational principles and deformation energies introduced for modelling beams undergoing large deformations and displacements. We then consider different kinds of loads treated in the literature and the corresponding induced beam deformations. We conclude by accounting for the available analysis for stability and some considerations about problems where live loads are applied, as well as by describing some relevant numerical methods of use in the applications we have in mind. The selection criterion for the reviewed papers is dictated by the need to study large deformations and the dynamics of pantographic sheets. (Large deformations of planar extensible beams and pantographic lattices: heuristic homogenization, experimental and numerical examples of equilibrium. Proc R Soc A 2016; 472(2185): 20150790), dell’Isola et al. (Designing a light fabric metamaterial being highly macroscopically tough under directional extension: first experimental evidence. Z Angew Math Phys 2015; 66(6): 3473–3498), Turco et al. (Hencky-type discrete model for pantographic structures: numerical comparison with second gradient continuum models. Z Angew Math Phys 2016; 67(4): 1–28)].
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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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Piekarska, W., M. Kubiak, Z. Saternus, S. Stano, and T. Domański. "Numerical Prediction Of Deformations In Laser Welded Sheets Made Of X5CrNi18-10 Steel." Archives of Metallurgy and Materials 60, no. 3 (September 1, 2015): 1965–72. http://dx.doi.org/10.1515/amm-2015-0334.
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AbstractThe work concerns the numerical modelling of coupled thermal and mechanical phenomena occurring in the laser beam welding process. Commercial Abaqus FEA engineering software is adopted to numerical computations in order to perform a comprehensive analysis of thermo-mechanical phenomena. Created in Fortran programming language additional numerical subroutines are implemented into Abaqus solver, used to describe the power intensity distribution of the movable laser beam heat source. Temperature dependent thermomechanical properties of X5CrNi18-10 steel are adopted in the numerical analysis of stress and strain states. Mathematical and numerical models are verified on the basis of a comparison between selected results of computer simulations and experimental studies on butt-welded joints.Numerical simulations are presented for steel sheet with a thickness of 2 mm. Temperature distributions, the shape and size of melted zone as well as residual stress and deformations are presented for analyzed elements. Numerically determined deflections are compared with the measured deflection of welded joint.
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Giacomini, Alessandro, and Marcello Ponsiglione. "Non-interpenetration of matter for SBV deformations of hyperelastic brittle materials." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 138, no. 5 (October 2008): 1019–41. http://dx.doi.org/10.1017/s0308210507000121.
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We prove that the Ciarlet–Nečas non-interpenetration of matter condition can be extended to the case of deformations of hyperelastic brittle materials belonging to the class of special functions of bounded variation (SBV), and can be taken into account for some variational models in fracture mechanics. In order to formulate such a condition, we define the deformed configuration under an SBV map by means of the approximately differentiable representative, and we prove some connected stability results under weak convergence. We provide an application to the case of brittle Ogden materials.
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Velmisov, Petr A., Yuliya A. Tamarova, and Yuliya V. Pokladova. "Investigation of the dynamic stability of bending-torsional deformations of the pipeline." Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva 23, no. 1 (March 31, 2021): 72–81. http://dx.doi.org/10.15507/2079-6900.23.202101.72-81.
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Nonlinear mathematical models are proposed that describe the dynamics of a pipeline with a fluid flowing in it: a) the model of bending-torsional vibrations with two degrees of freedom; b) the model describing flexural-torsional vibrations taking into account the nonlinearity of the bending moment and centrifugal force; c) the model that takes into account joint longitudinal, bending (transverse) and torsional vibrations. All proposed models are described by nonlinear partial differential equations for unknown strain functions. To describe the dynamics of a pipeline, the nonlinear theory of a rigid deformable body is used, which takes into account the transverse, tangential and longitudinal deformations of the pipeline. The dynamic stability of bending-torsional and longitudinal-flexural-torsional vibrations of the pipeline is investigated. The definitions of the stability of a deformable body adopted in this work correspond to the Lyapunov concept of stability of dynamical systems. The problem of studying dynamic stability, namely, stability according to initial data, is formulated as follows: at what values of the parameters characterizing the gas-body system, small deviations of the body from the equilibrium position at the initial moment of time will correspond to small deviations and at any moment of time. For the proposed models, positive definite functionals of the Lyapunov type are constructed, on the basis of which the dynamic stability of the pipeline is investigated. Sufficient stability conditions are obtained that impose restrictions on the parameters of a mechanical system.
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Buffa, Franco, Andrea Causin, Antonio Cazzani, Sergio Poppi, Giannina Sanna, Margherita Solci, Flavio Stochino, and Emilio Turco. "The Sardinia Radio Telescope: A comparison between close-range photogrammetry and finite element models." Mathematics and Mechanics of Solids 22, no. 5 (December 23, 2015): 1005–26. http://dx.doi.org/10.1177/1081286515616227.
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The Sardinia Radio Telescope (SRT), located near Cagliari (Italy), is the world’s second largest fully steerable radio telescope endowed with an active-surface system. Its primary mirror has a quasi-parabolic shape with a diameter of 64 m. The configuration of the primary mirror surface can be modified by means of electro-mechanical actuators. This capability ensures, within a fixed range, the balancing of the deformation caused, for example, by loads such as self-weight, thermal effects and wind pressure. In this way, the difference between the ideal shape of the mirror (which maximizes its performances) and the actual surface can be reduced. In this paper the authors describe the characteristics of the SRT, the close-range photogrammetry (CRP) survey developed in order to set up the actuator displacements, and a finite element model capable of accurately estimating the structural deformations. Numerical results are compared with CRP measurements in order to test the accuracy of the model.
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Ostanina, T. V., A. I. Shveykin, and P. V. Trusov. "The grain structure refinement of metals and alloys under severe plastic deformation: experimental data and analysis of mechanisms." PNRPU Mechanics Bulletin, no. 2 (December 15, 2020): 85–111. http://dx.doi.org/10.15593/perm.mech/2020.2.08.
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Wide opportunities of using fine-grained materials as structural and functional materials with advanced physical and mechanical properties have proved the importance of improving the existing technology and creating new processing methods and treatment conditions for such ma-terials. At the same time, a preliminary theoretical analysis using mathematical models gives an opportunity to significantly reduce the cost of such experimental studies. Thus, it is necessary to develop multilevel models of polycrystalline metals and alloys based on crystal plasticity with the description of structure, deformation mechanisms and refinement at various scale levels. To con-struct a correct model of such a class, it is necessary to analyze information and arrange a large amount of experimental data about grain structure refinement. The article presents a review of the experimental studies describing and analyzing the grain structure refinement during severe plastic deformations of various metal alloys. The refine-ment mainly occurs at low temperatures that are a priori lower than the temperatures at which re-crystallization becomes an important factor and the solid-state phase transitions may take place. We have summarized the significant physical mechanisms of the grain refinement during cold deformation based on the arranged experimental data from the review. All the considered articles pay attention to the local accumulation of lattice dislocations inside the grains (in the form of flat clusters), which leads to the lattice curvature and separation of grains into cells. As a result of a further accumulation of dislocations in the walls, there comes an increase in misorientation of the neighboring cells. The curved lattice is unstable (it seems clear that the flat clusters become a source of such curvatures) and relaxes with the formation and movement of the partial disclina-tions, which leads to the rotation of the adjacent grain regions and creation of new grain bounda-ries. In addition, the mesoscale defects located at the junctions of the grains (including the boundary intersection disclinations), flat clusters of the dislocations of the orientational mismatch at the grain boundaries and partial dislocations in the grains have a significant effect on the frag-mentation. The articles about the severe plastic deformation at high temperatures are briefly de-scribed here. It is noted that recrystallization is the main mechanism of the fine-grained structure formation under these conditions. We suggest including the description of the discussed mechanisms in the multilevel con-stitutive material models. When new experimental data appear for a specific process of the severe plastic deformation, the considered refinement mechanisms can be added.
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Forest, Samuel, and Karam Sab. "Finite-deformation second-order micromorphic theory and its relations to strain and stress gradient models." Mathematics and Mechanics of Solids 25, no. 7 (August 1, 2017): 1429–49. http://dx.doi.org/10.1177/1081286517720844.
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Germain’s general micromorphic theory of order [Formula: see text] is extended to fully non-symmetric higher-order tensor degrees of freedom. An interpretation of the microdeformation kinematic variables as relaxed higher-order gradients of the displacement field is proposed. Dynamical balance laws and hyperelastic constitutive equations are derived within the finite deformation framework. Internal constraints are enforced to recover strain gradient theories of grade [Formula: see text]. An extension to finite deformations of a recently developed stress gradient continuum theory is then presented, together with its relation to the second-order micromorphic model. The linearization of the combination of stress and strain gradient models is then shown to deliver formulations related to Eringen’s and Aifantis’s well-known gradient models involving the Laplacians of stress and strain tensors. Finally, the structures of the dynamical equations are given for strain and stress gradient media, showing fundamental differences in the dynamical behaviour of these two classes of generalized continua.
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Glaesener, Raphaël N., Claire Lestringant, Bastian Telgen, and Dennis M. Kochmann. "Continuum models for stretching- and bending-dominated periodic trusses undergoing finite deformations." International Journal of Solids and Structures 171 (October 2019): 117–34. http://dx.doi.org/10.1016/j.ijsolstr.2019.04.022.
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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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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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Sivtsev, N. S., and V. V. Tarasov. "Numerical Study of Stress-Strain State of Workpiece in Contact Problem of Surface Mandrel Drilling." Science & Technique 20, no. 3 (June 3, 2021): 259–67. http://dx.doi.org/10.21122/2227-1031-2021-20-3-259-267.
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In recent years, the economic factor has played an increasingly important role in the selection of technologies for manufacturing machine parts with specified values of normalized parameters of geometric accuracy and quality of working surfaces. As applied to surface plastic deformation processes, this is noticeably manifested in the search for effective friction control methods in the “tool – workpiece” pair, which ultimately determines the distribution pattern and the magnitude of stresses and strains in the workpiece and the tool. It is not possible to obtain a rigorous analytical solution to the problem of establishing a connection between surface conditions, friction, and the stress-strain state of the contacted bodies. In this regard, the construction of mathematical models comes to the fore, the solution of which is possible by numerical methods. The paper presents the results of a numerical study (computational experiment) of a finite-element model of workpiece deformation under various conditions of contact interaction and friction by one of the methods of surface plastic deformation – surface mandrel drilling. The friction coefficient has been chosen as the criterion for assessing the conditions of contact interaction and friction. It is shown that a change in the friction coefficient in the process of surface mandrel has no noticeable effect on the formation of a stress field in the deformable workpiece both in the axial, and in the radial and circumferential directions. At the same time, with an increase in the value of the friction coefficient in the “tool – workpiece” pair and with the associated increase in the force of mechanical resistance to deformation of the workpiece, their growth is observed. A computational experiment has confirmed the presence of non-contact deformations of the workpiece and tool during surface mandrel drilling, as well as as a decrease in the value of residual deformations in the workpiece with a decrease in the coefficient of friction. Balance assessment of contact surface displacements in the workpiece (the inner surface of the hole to be machined) and the tool (mandrel) has shown that the deformations of the tool in the elastic region can lead to a significant decrease in the real tightness of surface mandrel drilling.
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Jafari Bidhendi, Amirhossein, and Rami K. Korhonen. "A Finite Element Study of Micropipette Aspiration of Single Cells: Effect of Compressibility." Computational and Mathematical Methods in Medicine 2012 (2012): 1–9. http://dx.doi.org/10.1155/2012/192618.
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Micropipette aspiration (MA) technique has been widely used to measure the viscoelastic properties of different cell types. Cells experience nonlinear large deformations during the aspiration procedure. Neo-Hookean viscohyperelastic (NHVH) incompressible and compressible models were used to simulate the creep behavior of cells in MA, particularly accounting for the effect of compressibility, bulk relaxation, and hardening phenomena under large strain. In order to find optimal material parameters, the models were fitted to the experimental data available for mesenchymal stem cells. Finally, through Neo-Hookean porohyperelastic (NHPH) material model for the cell, the influence of fluid flow on the aspiration length of the cell was studied. Based on the results, we suggest that the compressibility and bulk relaxation/fluid flow play a significant role in the deformation behavior of single cells and should be taken into account in the analysis of the mechanics of cells.
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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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Dosaev, Marat, Vitaly Samsonov, and Vladislav Bekmemetev. "Comparison between 2D and 3D Simulation of Contact of Two Deformable Axisymmetric Bodies." International Journal of Nonlinear Sciences and Numerical Simulation 21, no. 2 (April 26, 2020): 123–33. http://dx.doi.org/10.1515/ijnsns-2018-0157.
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AbstractA portable pneumatic video-tactile sensor for determining the local stiffness of soft tissue and the methodology for its application are considered. The expected range of local elastic modulus that can be estimated by the sensor is 100 kPa–1 MPa. The current version of the device is designed to determine the characteristics of tissues that are close in mechanical properties to the skin with subcutis and muscles. A numerical simulation of the contact between the sensor head and the soft tissue was performed using the finite-element method. Both 2D and 3D models were developed. Results of experiments with device prototype are used for approval of adequacy of mathematical modelling in case of large deformations. Simulation results can be used to create soft tissue databases, which will be required to determine the local stiffness of soft tissues by the sensor. 2D model proved to be more efficient for the chosen range of values of local stiffness of soft tissues.
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Snoeijer, J. H., A. Pandey, M. A. Herrada, and J. Eggers. "The relationship between viscoelasticity and elasticity." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476, no. 2243 (November 2020): 20200419. http://dx.doi.org/10.1098/rspa.2020.0419.
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Soft materials that are subjected to large deformations exhibit an extremely rich phenomenology, with properties lying in between those of simple fluids and those of elastic solids. In the continuum description of these systems, one typically follows either the route of solid mechanics (Lagrangian description) or the route of fluid mechanics (Eulerian description). The purpose of this review is to highlight the relationship between the theories of viscoelasticity and of elasticity, and to leverage this connection in contemporary soft matter problems. We review the principles governing models for viscoelastic liquids, for example solutions of flexible polymers. Such materials are characterized by a relaxation time λ , over which stresses relax. We recall the kinematics and elastic response of large deformations, and show which polymer models do (and which do not) correspond to a nonlinear elastic solid in the limit λ → ∞. With this insight, we split the work done by elastic stresses into reversible and dissipative parts, and establish the general form of the conservation law for the total energy. The elastic correspondence can offer an insightful tool for a broad class of problems; as an illustration, we show how the presence or absence of an elastic limit determines the fate of an elastic thread during capillary instability.
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Gao, X. L., X. N. Jing, and G. Subhash. "Two new expanding cavity models for indentation deformations of elastic strain-hardening materials." International Journal of Solids and Structures 43, no. 7-8 (April 2006): 2193–208. http://dx.doi.org/10.1016/j.ijsolstr.2005.03.062.
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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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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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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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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.
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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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Stempin, Paulina, and Wojciech Sumelka. "Formulation and experimental validation of space-fractional Timoshenko beam model with functionally graded materials effects." Computational Mechanics 68, no. 3 (March 13, 2021): 697–708. http://dx.doi.org/10.1007/s00466-021-01987-6.
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AbstractIn this study, the static bending behaviour of a size-dependent thick beam is considered including FGM (Functionally Graded Materials) effects. The presented theory is a further development and extension of the space-fractional (non-local) Euler–Bernoulli beam model (s-FEBB) to space-fractional Timoshenko beam (s-FTB) one by proper taking into account shear deformation. Furthermore, a detailed parametric study on the influence of length scale and order of fractional continua for different boundary conditions demonstrates, how the non-locality affects the static bending response of the s-FTB model. The differences in results between s-FTB and s-FEBB models are shown as well to indicate when shear deformations need to be considered. Finally, material parameter identification and validation based on the bending of SU-8 polymer microbeams confirm the effectiveness of the presented model.
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Szekely, Julian. "Mathematical Modeling in Materials Science and Engineering." MRS Bulletin 19, no. 1 (January 1994): 11–13. http://dx.doi.org/10.1557/s0883769400038793.
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During the past two decades, mathematical modeling has been gaining acceptance as a legitimate part of materials science and engineering. However, as common to all relatively new disciplines, we still lack a realistic perspective regarding the uses, limitations, and even the optimal methodologies of mathematical modeling techniques.The term “mathematical modeling” covers a broad range of activities, including molecular dynamics, other atomistic scale systems, continuum fluid and solid mechanics, deformation processing, systems analysis, input-output models, and lifecycle analyses. The common point is that we use algebraic expressions or differential equations to represent physical systems to varying degrees of approximation and then manipulate these equations, using computers, to obtain graphical output.While it is becoming an accepted fact that some kind of mathematical modeling will be needed to make most research programs complete, there is still considerable ambiguity as to what form this should take and what might be the actual usefulness of such an effort.Among the more seasoned and successful practitioners of this art, clear guidelines have emerged regarding the uses and limitations of the mathematical modeling approach. We seek to illustrate these uses through the successful modeling examples presented by some leading practitioners. Some general principles may be worth repeating as an introduction to this interesting collection of articles.
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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.
Full textAbstract:
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