This paper presents a nonlinear micropolar nonclassical continuum theory (MPNCCT) for finite deformation, finite strain deformation physics of thermosviscoelastic solid medium with memory (polymeric micropolar solids)...This paper presents a nonlinear micropolar nonclassical continuum theory (MPNCCT) for finite deformation, finite strain deformation physics of thermosviscoelastic solid medium with memory (polymeric micropolar solids) based on classical rotations cΘand their rates. Contravariant second Piola-Kirchhoff stress and moment tensors, in conjunction with finite deformation measures derived by the authors in recent paper, are utilized in deriving the conservation and balance laws and the constitutive theories based on conjugate pairs in entropy inequality and the representation theorem. This nonlinear MPNCCT for TVES with rheology: 1) incorporates nonlinear ordered rate dissipation mechanism based on Green’s strain rates up to order n;2) also incorporates an additional ordered rate dissipation mechanism due to microconstituents, the viscosity of the medium and the rates of the symmetric part of the rotation gradient (of cΘ) tensor up to order n, referred to as micropolar dissipation or micropolar viscous dissipation mechanism;3) incorporates the primary mechanism of memory or rheology due to long chain molecules of the polymer and the viscosity of the medium by using the contravaraint second Piola-Kirchhoff stress tensor and its rates up to order m, resulting in a relaxation spectrum;4) incorporates second mechanism of memory or rheology due to nonclassical physics, interaction of microconstituents with the viscous medium and long chain molecules by considering rates of the contravariant second Piola-Kirchhoff moment tensor up to order m, resulting in relaxation of second Piola-Kirchhoff moment tensor. This results in another relaxation spectrum for the second Piola-Kirchhoff moment tensor due to microconstituents, referred to as micropolar relaxation spectrum consisting of micropolar relaxation time constants of the material. This nonlinear MPNCCT for TVES with memory is thermodynamically and mathematically consistent, and the mathematical model consisting of conservation and balance laws and the constitutive theories has closure and naturally reduces to linear MPNCCT based on infinitesimal deformation assumption. BMM is the essential balance law for all MPNCCT and is used in the present work as well. In the absence of this balance law, a valid thermodynamically and mathematically consistent nonlinear MPNCCT is not possible. The nonlinear MPNCCT based on rotations (cΘ+αΘ) and αΘ(ignoring cΘ) is not considered due to the fact that even the linear MPNCCT based on these rotations is invalid and is thermodynamically and mathematically inconsistent MPNCCT.展开更多
The theory of plasticity as a special field of continuum mechanics deals with the irreversible,i.e.permanent,deformation of solids.Under the action of given loads or deformations,the state of the stresses and strains ...The theory of plasticity as a special field of continuum mechanics deals with the irreversible,i.e.permanent,deformation of solids.Under the action of given loads or deformations,the state of the stresses and strains or the strain rates in these bodies is described.In this way,it complements the theory of elasticity for the reversible behavior of solids.In practice,it has been observed that many materials behave elastically up to a certain load(yield point),beyond that load,however,increasingly plastic or liquid-like.The combination of these two material properties is known as elastoplasticity.The classical elastoplastic material behavior is assumed to be time-independent or rate-independent.In contrast,we call a time-or rate-dependent behavior visco-elastoplastic and visco-plastic—if the elastic part of the deformation is neglected.In plasticity theory,because of the given loads the states of the state variables stress,strain and temperature as well as their changes are described.For this purpose,the observed phenomena are introduced and put into mathematical relationships.The constitutive relations describing the specific material behavior are finally embedded in the fundamental relations of continuum theory and physics.Historically,the theory of plasticity was introduced in order to better estimate the strength of constructions.An analysis based purely on elastic codes is not in a position to do this,and can occasionally even lead to incorrect interpretations.On the other hand,the entire field of forming techniques requires a theory for the description of plastic behavior.Starting from the classical description of plastic behavior with small deformations,the present review is intended to provide an insight into the state of the art when taking into account finite deformations.展开更多
The overbroken rock mass of gob areas is made up of broken and accumulated rock blocks compressed to some extent by the overlying strata. The beating pressure of the gob can directly affect the safety of mining fields...The overbroken rock mass of gob areas is made up of broken and accumulated rock blocks compressed to some extent by the overlying strata. The beating pressure of the gob can directly affect the safety of mining fields, formarion of road retained along the next goaf and seepage of water and methane through the gob. In this paper, the software RFPA＇2000 is used to construct numerical models. Especially the Euler method of control volume is proposed to solve the simulation difficulty arising from plastically finite deformations. The results show that three characteristic regions occurred in the gob area： （1） a naturally accumulated region, 0-10 m away from unbroken surrounding rock walls, where the beating pressure is nearly zero; （2） an overcompacted region, 10-20 m away from unbroken walls, where the beating pressure results in the maximum value of the gob area; （3） a stable compaction region, more than 20 m away from unbroken walls and occupying absolutely most of the gob area, where the beating pressures show basically no differences. Such a characteristic can exolain the easy-seeoaged “O”-ring phenomena around mining fields very well.展开更多
A nonlinear wave equation of elastic rod taking account of finite deformation, transverse inertia and shearing strain is derived by means of the Hamilton principle in this paper. Nonlinear wave equation and truncated ...A nonlinear wave equation of elastic rod taking account of finite deformation, transverse inertia and shearing strain is derived by means of the Hamilton principle in this paper. Nonlinear wave equation and truncated nonlinear wave equation are solved by the Jacobi elliptic sine function expansion and the third kind of Jacobi elliptic function expansion method. The exact periodic solutions of these nonlinear equations are obtained, including the shock wave solution and the solitary wave solution. The necessary condition of exact periodic solutions, shock solution and solitary solution existence is discussed.展开更多
On the basis of classical linear theory on longitudinal, torsional and flexural waves in thin elastic rods, and taking finite deformation and dispersive effects into consideration, three kinds of nonlinear evolution e...On the basis of classical linear theory on longitudinal, torsional and flexural waves in thin elastic rods, and taking finite deformation and dispersive effects into consideration, three kinds of nonlinear evolution equations are derived. Qualitative analysis of three kinds of nonlinear equations are presented. It is shown that these equations have homoclinic or heteroclinic orbits on the phase plane, corresponding to solitary wave or shock wave solutions, respectively. Based on the principle of homogeneous balance, these equations are solved with the Jacobi elliptic function expansion method. Results show that existence of solitary wave solution and shock wave solution is possible under certain conditions. These conclusions are consistent with qualitative analysis.展开更多
It is noted that the behavior of most piezoelectric materials is temperaturedependent and such piezo-thermo-elastic coupling phenomenon has become even more pronounced in thecase of finite deformation. On the other ha...It is noted that the behavior of most piezoelectric materials is temperaturedependent and such piezo-thermo-elastic coupling phenomenon has become even more pronounced in thecase of finite deformation. On the other hand, for the purpose of precise shape and vibrationcontrol of piezoelectric smart structures, their deformation under external excitation must beideally modeled. This demands a thorough study of the coupled piezo-thermo-elastic response underfinite deformation. In this study, the governing equations of piezoelectric structures areformulated through the theory of virtual displacement principle and a finite element method isdeveloped. It should be emphasized that in the finite element method the fully coupledpiezo-thermo-elastic behavior and the geometric non-linearity are considered. The method developedis then applied to simulate the dynamic and steady response of a clamped plate to heat flux actingon one side of the plate to mimic the behavior of a battery plate of satellite irradiated under thesun. The results obtained are compared against classical solutions, whereby the thermal conductivityis assumed to be independent of deformation. It is found that the full-coupled theory predicts lesstransient response of the temperature compared to the classic analysis. In the steady state limit,the predicted temperature distribution within the plate for small heat flux is almost the same forboth analyses. However, it is noted that increasing the heat flux will increase the deviationbetween the predictions of the temperature distribution by the full coupled theory and by theclassic analysis. It is concluded from the present study that, in order to precisely predict thedeformation of smart structures, the piezo-thermo-elastic coupling, geometric non-linearity and thedeformation dependent thermal conductivity should be taken into account.展开更多
A series of monotonic tensile experiments of thermo-induced shape memory polyurethane （TSMPU） at different loading rates were carried out to investigate the interaction between the internal heat production and the m...A series of monotonic tensile experiments of thermo-induced shape memory polyurethane （TSMPU） at different loading rates were carried out to investigate the interaction between the internal heat production and the mechanical deformation. It is shown that the tem- perature variation on the surfaces of the specimens due to the internal heat production affects the mechanical properties of TSMPU remarkably. Then, based on irreversible thermodynamics, the Helmholtz free energy was decomposed into three parts, i.e., the instantaneous elastic free energy, visco-plastic free energy and heat free energy. The total deformation gradient was decomposed into the mechanical and thermal parts, and the mechanical deformation gradient was further divided into the elastic and visco-plastic components. The Hencky＇s logarithmic strain was used in the current configuration. The heat equilibrium equation of internal heat production and heat exchange was derived in accordance with the first and second thermodynamics laws. The temperature of specimens was contributed by the internal heat production and the ambient temperature simultaneously, and a thermo-mechanically coupled thermo-elasto-visco-plastie model was established. The effect of temperature variation of specimens on the mechanical properties of the material was considered in this work. Finally, the capability of the proposed model was validated by comparing the simulated results with the corresponding experimental data of TSMPU.展开更多
The problem of finite deformation of an incompressible rectangular rubber ring with an internal rigid body, where the ring is subjected to equal axial loads at its two ends, is examined. A reasonable mathematical mode...The problem of finite deformation of an incompressible rectangular rubber ring with an internal rigid body, where the ring is subjected to equal axial loads at its two ends, is examined. A reasonable mathematical model is formulated by using the nonlinear field theory and the implicit analytical solutions are derived. Then numerical simulations are implemented to further illustrate the results and obtain some meaningful conclusions. The deformation of the lateral surface of the ring becomes larger with the increasing axial loads, the decreasing ratio of the inner and outer radii and the increasing height of the ring.展开更多
Recently,numerous studies have demonstrated that the physics-informed neural network(PINN)can effectively and accurately resolve hyperelastic finite deformation problems.In this paper,a PINN framework for tackling hyp...Recently,numerous studies have demonstrated that the physics-informed neural network(PINN)can effectively and accurately resolve hyperelastic finite deformation problems.In this paper,a PINN framework for tackling hyperelastic-magnetic coupling problems is proposed.Since the solution space consists of two-phase domains,two separate networks are constructed to independently predict the solution for each phase region.In addition,a conscious point allocation strategy is incorporated to enhance the prediction precision of the PINN in regions characterized by sharp gradients.With the developed framework,the magnetic fields and deformation fields of magnetorheological elastomers(MREs)are solved under the control of hyperelastic-magnetic coupling equations.Illustrative examples are provided and contrasted with the reference results to validate the predictive accuracy of the proposed framework.Moreover,the advantages of the proposed framework in solving hyperelastic-magnetic coupling problems are validated,particularly in handling small data sets,as well as its ability in swiftly and precisely forecasting magnetostrictive motion.展开更多
Based on the Reddy's theory of plates with the effect of higher-order shear deformations, the governing equations for bending of orthotropic plates with finite deformations were established. The differential quadr...Based on the Reddy's theory of plates with the effect of higher-order shear deformations, the governing equations for bending of orthotropic plates with finite deformations were established. The differential quadrature (DQ) method of nonlinear analysis to the problem was presented. New DQ approach, presented by Wang and Bert (DQWB), is extended to handle the multiple boundary conditions of plates. The techniques were also further extended to simplify nonlinear computations. The numerical convergence and comparison of solutions were studied. The results show that the DQ method presented is very reliable and valid. Moreover, the influences of geometric and material parameters as well as the transverse shear deformations on nonlinear bending were investigated. Numerical results show the influence of the shear deformation on the static bending of orthotropic moderately thick plate is significant.展开更多
In this paper, based on the finite deformation S-R decomposition theorem, the definition of the body moment is renewed as the stem of its internal and external. The expression of the increment rate of the deformation ...In this paper, based on the finite deformation S-R decomposition theorem, the definition of the body moment is renewed as the stem of its internal and external. The expression of the increment rate of the deformation energy is derived and the physical meaning is clarified. The power variational principle and the complementary power variational principle for finite deformation mechanics are supplemented and perfected.展开更多
This paper proposes a geometrically nonlinear total Lagrangian Galerkin meshfree formulation based on the stabilized conforming nodal integration for efficient analysis of shear deformable beam.The present nonlinear a...This paper proposes a geometrically nonlinear total Lagrangian Galerkin meshfree formulation based on the stabilized conforming nodal integration for efficient analysis of shear deformable beam.The present nonlinear analysis encompasses the fully geometric nonlinearities due to large deflection,large deformation as well as finite rotation.The incremental equilibrium equation is obtained by the consistent linearization of the nonlinear variational equation.The Lagrangian meshfree shape function is utilized to discretize the variational equation.Subsequently to resolve the shear and membrane locking issues and accelerate the computation,the method of stabilized conforming nodal integration is systematically implemented through the Lagrangian gradient smoothing operation.Numerical results reveal that the present formulation is very effective.展开更多
Based on the general solution given to a kind of linear tensor equations,the spin of a symmetric tensor is derived in an invariant form.The result is applied to find the spins of the left and the tight stretch tensors...Based on the general solution given to a kind of linear tensor equations,the spin of a symmetric tensor is derived in an invariant form.The result is applied to find the spins of the left and the tight stretch tensors and the relation among different rotation rate tensors has been discussed.According to work conjugacy,the relations between Cauchy stress and the stresses conjugate to Hill's generalized strains are obtained.Particularly,the logarithmic strain,its time rate and the conjugate stress have been discussed in de- tail.These results are important in modeling the constitutive relations for finite deformations in continuum me- chanics.展开更多
The differences between finite deformation and infinitesimal deformation are discussed. They are exercised on elasto-viscoplastic constitutive relations of concrete. Then, a rate-dependent mechanics model was presente...The differences between finite deformation and infinitesimal deformation are discussed. They are exercised on elasto-viscoplastic constitutive relations of concrete. Then, a rate-dependent mechanics model was presented on the basis of Ottosen's four-parameter yield criterion, where different loading surface transferring laws were taken into account, when material was in hardening stage or in softening stage, respectively. The model is well established, so that it can be applied to simulate the response of concrete subject to impact loading. Green-Naghdi stress rate was introduced as objective stress rate. Appropriate hypothesis was postulated in accordance with many experimental results, which could reflect the mechanical behaviour of concrete with large deformation. Available thoughts as well as effective methods are also provided for the research on related engineering problems.展开更多
A new nonlinear wave equation of a finite deformation elastic circular rod simultaneously introducing transverse inertia and shearing strain was derived by means of Hamilton principle. The nonlinear equation includes ...A new nonlinear wave equation of a finite deformation elastic circular rod simultaneously introducing transverse inertia and shearing strain was derived by means of Hamilton principle. The nonlinear equation includes two nonlinear terms caused by finite deformation and double geometric dispersion effects caused by transverse inertia and transverse shearing strain. Nonlinear wave equation and corresponding truncated nonlinear wave equation were solved by the hyperbolic secant function finite expansion method. The solitary wave solutions of these nonlinear equations were obtained. The necessary condition of these solutions existence was given also.展开更多
Whether the concept of effective stress and strain in elastic-plastic theory is still valid under the condition of finite deformation was mainly discussed. The uni-axial compression experiments in plane stress and pla...Whether the concept of effective stress and strain in elastic-plastic theory is still valid under the condition of finite deformation was mainly discussed. The uni-axial compression experiments in plane stress and plane strain states were chosen for study. In the two kinds of stress states, the stress-strain curve described by logarithm strain and rotated Kirchhoff stress matches the experiments data better than the curves defined by other stress-strain description.展开更多
An algorithm for integrating the constitutive equations in thermal framework is presented, in which the plastic deformation gradient is chosen as the integration variable. Compared with the classic algorithm, a key fe...An algorithm for integrating the constitutive equations in thermal framework is presented, in which the plastic deformation gradient is chosen as the integration variable. Compared with the classic algorithm, a key feature of this new approach is that it can describe the finite deformation of crystals under thermal conditions. The obtained plastic deformation gradient contains not only plastic defor- mation but also thermal effects. The governing equation for the plastic deformation gradient is obtained based on ther- mal multiplicative decomposition of the total deformation gradient. An implicit method is used to integrate this evo- lution equation to ensure stability. Single crystal 1 100 aluminum is investigated to demonstrate practical applications of the model. The effects of anisotropic properties, time step, strain rate and temperature are calculated using this integration model.展开更多
By combining grain boundary (GB) and its influence zone, a micromechanic model for polycrystal is established for considering the influence of GB. By using the crystal plasticity theory and the finite element method f...By combining grain boundary (GB) and its influence zone, a micromechanic model for polycrystal is established for considering the influence of GB. By using the crystal plasticity theory and the finite element method for finite deformation, numerical simulation is carried out by the model. Calculated results display the microscopic characteristic of deformation fields of grains and are in qualitative agreement with experimental results.展开更多
This paper concerns the dynamic plastic response of a circular plate resting on fluid subjected to a uniformly distributed rectangular load pulse with finite deformation. It is assumed that the fluid is incompressible...This paper concerns the dynamic plastic response of a circular plate resting on fluid subjected to a uniformly distributed rectangular load pulse with finite deformation. It is assumed that the fluid is incompressible and inviscous, and the plate is made of rigid-plastic material and simply supported along its edge. By using the method of the Hankel integral transformation, the nonuniform fluid resistance is derived as the plate and the fluid is coupled. Finally, an analytic solution for a circular plate under a medium load is obtained according to the equations of motion of the plate with finite deformation.展开更多
By using the logarithmic strain, the finite deformation plastic theory, corresponding to the infinitesimal plastic theory, is established successively. The plastic consistent algorithm with first order accuracy for th...By using the logarithmic strain, the finite deformation plastic theory, corresponding to the infinitesimal plastic theory, is established successively. The plastic consistent algorithm with first order accuracy for the finite element method (FEM) is developed. Numerical examples are presented to illustrate the validity of the theory and effectiveness of the algorithm.展开更多
文摘This paper presents a nonlinear micropolar nonclassical continuum theory (MPNCCT) for finite deformation, finite strain deformation physics of thermosviscoelastic solid medium with memory (polymeric micropolar solids) based on classical rotations cΘand their rates. Contravariant second Piola-Kirchhoff stress and moment tensors, in conjunction with finite deformation measures derived by the authors in recent paper, are utilized in deriving the conservation and balance laws and the constitutive theories based on conjugate pairs in entropy inequality and the representation theorem. This nonlinear MPNCCT for TVES with rheology: 1) incorporates nonlinear ordered rate dissipation mechanism based on Green’s strain rates up to order n;2) also incorporates an additional ordered rate dissipation mechanism due to microconstituents, the viscosity of the medium and the rates of the symmetric part of the rotation gradient (of cΘ) tensor up to order n, referred to as micropolar dissipation or micropolar viscous dissipation mechanism;3) incorporates the primary mechanism of memory or rheology due to long chain molecules of the polymer and the viscosity of the medium by using the contravaraint second Piola-Kirchhoff stress tensor and its rates up to order m, resulting in a relaxation spectrum;4) incorporates second mechanism of memory or rheology due to nonclassical physics, interaction of microconstituents with the viscous medium and long chain molecules by considering rates of the contravariant second Piola-Kirchhoff moment tensor up to order m, resulting in relaxation of second Piola-Kirchhoff moment tensor. This results in another relaxation spectrum for the second Piola-Kirchhoff moment tensor due to microconstituents, referred to as micropolar relaxation spectrum consisting of micropolar relaxation time constants of the material. This nonlinear MPNCCT for TVES with memory is thermodynamically and mathematically consistent, and the mathematical model consisting of conservation and balance laws and the constitutive theories has closure and naturally reduces to linear MPNCCT based on infinitesimal deformation assumption. BMM is the essential balance law for all MPNCCT and is used in the present work as well. In the absence of this balance law, a valid thermodynamically and mathematically consistent nonlinear MPNCCT is not possible. The nonlinear MPNCCT based on rotations (cΘ+αΘ) and αΘ(ignoring cΘ) is not considered due to the fact that even the linear MPNCCT based on these rotations is invalid and is thermodynamically and mathematically inconsistent MPNCCT.
文摘The theory of plasticity as a special field of continuum mechanics deals with the irreversible,i.e.permanent,deformation of solids.Under the action of given loads or deformations,the state of the stresses and strains or the strain rates in these bodies is described.In this way,it complements the theory of elasticity for the reversible behavior of solids.In practice,it has been observed that many materials behave elastically up to a certain load(yield point),beyond that load,however,increasingly plastic or liquid-like.The combination of these two material properties is known as elastoplasticity.The classical elastoplastic material behavior is assumed to be time-independent or rate-independent.In contrast,we call a time-or rate-dependent behavior visco-elastoplastic and visco-plastic—if the elastic part of the deformation is neglected.In plasticity theory,because of the given loads the states of the state variables stress,strain and temperature as well as their changes are described.For this purpose,the observed phenomena are introduced and put into mathematical relationships.The constitutive relations describing the specific material behavior are finally embedded in the fundamental relations of continuum theory and physics.Historically,the theory of plasticity was introduced in order to better estimate the strength of constructions.An analysis based purely on elastic codes is not in a position to do this,and can occasionally even lead to incorrect interpretations.On the other hand,the entire field of forming techniques requires a theory for the description of plastic behavior.Starting from the classical description of plastic behavior with small deformations,the present review is intended to provide an insight into the state of the art when taking into account finite deformations.
基金Projects 2005CB221502 supported by the Vital Foundational 973 Program of China, 50225414 by the National Outstanding Youth Foundation,20040350222 by China Postdoctoral Science FoundationBK 2004033 by Jiangsu Natural Science Foundation
文摘The overbroken rock mass of gob areas is made up of broken and accumulated rock blocks compressed to some extent by the overlying strata. The beating pressure of the gob can directly affect the safety of mining fields, formarion of road retained along the next goaf and seepage of water and methane through the gob. In this paper, the software RFPA＇2000 is used to construct numerical models. Especially the Euler method of control volume is proposed to solve the simulation difficulty arising from plastically finite deformations. The results show that three characteristic regions occurred in the gob area： （1） a naturally accumulated region, 0-10 m away from unbroken surrounding rock walls, where the beating pressure is nearly zero; （2） an overcompacted region, 10-20 m away from unbroken walls, where the beating pressure results in the maximum value of the gob area; （3） a stable compaction region, more than 20 m away from unbroken walls and occupying absolutely most of the gob area, where the beating pressures show basically no differences. Such a characteristic can exolain the easy-seeoaged “O”-ring phenomena around mining fields very well.
基金Project supported by the National Natural Science Foundation of China (No. 10472076).
文摘A nonlinear wave equation of elastic rod taking account of finite deformation, transverse inertia and shearing strain is derived by means of the Hamilton principle in this paper. Nonlinear wave equation and truncated nonlinear wave equation are solved by the Jacobi elliptic sine function expansion and the third kind of Jacobi elliptic function expansion method. The exact periodic solutions of these nonlinear equations are obtained, including the shock wave solution and the solitary wave solution. The necessary condition of exact periodic solutions, shock solution and solitary solution existence is discussed.
基金Project supported by the National Natural Science Foundation of China (No.10772129)the Youth Science Foundation of Shanxi Province of China (No.2006021005)
文摘On the basis of classical linear theory on longitudinal, torsional and flexural waves in thin elastic rods, and taking finite deformation and dispersive effects into consideration, three kinds of nonlinear evolution equations are derived. Qualitative analysis of three kinds of nonlinear equations are presented. It is shown that these equations have homoclinic or heteroclinic orbits on the phase plane, corresponding to solitary wave or shock wave solutions, respectively. Based on the principle of homogeneous balance, these equations are solved with the Jacobi elliptic function expansion method. Results show that existence of solitary wave solution and shock wave solution is possible under certain conditions. These conclusions are consistent with qualitative analysis.
基金the National Natural Science Foundation of China (Nos.10132010 and 50135030)the Foundation of In-service Doctors of Xi'an Jiaotong University
文摘It is noted that the behavior of most piezoelectric materials is temperaturedependent and such piezo-thermo-elastic coupling phenomenon has become even more pronounced in thecase of finite deformation. On the other hand, for the purpose of precise shape and vibrationcontrol of piezoelectric smart structures, their deformation under external excitation must beideally modeled. This demands a thorough study of the coupled piezo-thermo-elastic response underfinite deformation. In this study, the governing equations of piezoelectric structures areformulated through the theory of virtual displacement principle and a finite element method isdeveloped. It should be emphasized that in the finite element method the fully coupledpiezo-thermo-elastic behavior and the geometric non-linearity are considered. The method developedis then applied to simulate the dynamic and steady response of a clamped plate to heat flux actingon one side of the plate to mimic the behavior of a battery plate of satellite irradiated under thesun. The results obtained are compared against classical solutions, whereby the thermal conductivityis assumed to be independent of deformation. It is found that the full-coupled theory predicts lesstransient response of the temperature compared to the classic analysis. In the steady state limit,the predicted temperature distribution within the plate for small heat flux is almost the same forboth analyses. However, it is noted that increasing the heat flux will increase the deviationbetween the predictions of the temperature distribution by the full coupled theory and by theclassic analysis. It is concluded from the present study that, in order to precisely predict thedeformation of smart structures, the piezo-thermo-elastic coupling, geometric non-linearity and thedeformation dependent thermal conductivity should be taken into account.
基金Financial supports by National Natural Science Foundation of China (11572265,11202171)Excellent Youth Found of Sichuan Province (2017JQ0019)+1 种基金Open Project of Traction Power State Key Laboratory(TPL1606)Exploration Project of Traction Power State Key Laboratory (2017TPL_T04)
文摘A series of monotonic tensile experiments of thermo-induced shape memory polyurethane （TSMPU） at different loading rates were carried out to investigate the interaction between the internal heat production and the mechanical deformation. It is shown that the tem- perature variation on the surfaces of the specimens due to the internal heat production affects the mechanical properties of TSMPU remarkably. Then, based on irreversible thermodynamics, the Helmholtz free energy was decomposed into three parts, i.e., the instantaneous elastic free energy, visco-plastic free energy and heat free energy. The total deformation gradient was decomposed into the mechanical and thermal parts, and the mechanical deformation gradient was further divided into the elastic and visco-plastic components. The Hencky＇s logarithmic strain was used in the current configuration. The heat equilibrium equation of internal heat production and heat exchange was derived in accordance with the first and second thermodynamics laws. The temperature of specimens was contributed by the internal heat production and the ambient temperature simultaneously, and a thermo-mechanically coupled thermo-elasto-visco-plastie model was established. The effect of temperature variation of specimens on the mechanical properties of the material was considered in this work. Finally, the capability of the proposed model was validated by comparing the simulated results with the corresponding experimental data of TSMPU.
基金supported by the National Natural Science Foundation of China (Nos. 10872045, 10721062 and 10772104)the Program for New Century Excellent Talents in University (No. NCET-09-0096)the Fundamental Research Funds for the Central Universities
文摘The problem of finite deformation of an incompressible rectangular rubber ring with an internal rigid body, where the ring is subjected to equal axial loads at its two ends, is examined. A reasonable mathematical model is formulated by using the nonlinear field theory and the implicit analytical solutions are derived. Then numerical simulations are implemented to further illustrate the results and obtain some meaningful conclusions. The deformation of the lateral surface of the ring becomes larger with the increasing axial loads, the decreasing ratio of the inner and outer radii and the increasing height of the ring.
基金supported by the National Natural Science Foundation of China(Nos.12072105 and 11932006)。
文摘Recently,numerous studies have demonstrated that the physics-informed neural network(PINN)can effectively and accurately resolve hyperelastic finite deformation problems.In this paper,a PINN framework for tackling hyperelastic-magnetic coupling problems is proposed.Since the solution space consists of two-phase domains,two separate networks are constructed to independently predict the solution for each phase region.In addition,a conscious point allocation strategy is incorporated to enhance the prediction precision of the PINN in regions characterized by sharp gradients.With the developed framework,the magnetic fields and deformation fields of magnetorheological elastomers(MREs)are solved under the control of hyperelastic-magnetic coupling equations.Illustrative examples are provided and contrasted with the reference results to validate the predictive accuracy of the proposed framework.Moreover,the advantages of the proposed framework in solving hyperelastic-magnetic coupling problems are validated,particularly in handling small data sets,as well as its ability in swiftly and precisely forecasting magnetostrictive motion.
文摘Based on the Reddy's theory of plates with the effect of higher-order shear deformations, the governing equations for bending of orthotropic plates with finite deformations were established. The differential quadrature (DQ) method of nonlinear analysis to the problem was presented. New DQ approach, presented by Wang and Bert (DQWB), is extended to handle the multiple boundary conditions of plates. The techniques were also further extended to simplify nonlinear computations. The numerical convergence and comparison of solutions were studied. The results show that the DQ method presented is very reliable and valid. Moreover, the influences of geometric and material parameters as well as the transverse shear deformations on nonlinear bending were investigated. Numerical results show the influence of the shear deformation on the static bending of orthotropic moderately thick plate is significant.
文摘In this paper, based on the finite deformation S-R decomposition theorem, the definition of the body moment is renewed as the stem of its internal and external. The expression of the increment rate of the deformation energy is derived and the physical meaning is clarified. The power variational principle and the complementary power variational principle for finite deformation mechanics are supplemented and perfected.
基金supported by the National Natural Science Foundation of China(10972188)the Program for New Century Excellent Talents in University from China Education Ministry(NCET-09-0678)
文摘This paper proposes a geometrically nonlinear total Lagrangian Galerkin meshfree formulation based on the stabilized conforming nodal integration for efficient analysis of shear deformable beam.The present nonlinear analysis encompasses the fully geometric nonlinearities due to large deflection,large deformation as well as finite rotation.The incremental equilibrium equation is obtained by the consistent linearization of the nonlinear variational equation.The Lagrangian meshfree shape function is utilized to discretize the variational equation.Subsequently to resolve the shear and membrane locking issues and accelerate the computation,the method of stabilized conforming nodal integration is systematically implemented through the Lagrangian gradient smoothing operation.Numerical results reveal that the present formulation is very effective.
基金The project is supported by the National Natural Science Foundation of Chinathe Chinese Academy of Sciences(No.87-52)
文摘Based on the general solution given to a kind of linear tensor equations,the spin of a symmetric tensor is derived in an invariant form.The result is applied to find the spins of the left and the tight stretch tensors and the relation among different rotation rate tensors has been discussed.According to work conjugacy,the relations between Cauchy stress and the stresses conjugate to Hill's generalized strains are obtained.Particularly,the logarithmic strain,its time rate and the conjugate stress have been discussed in de- tail.These results are important in modeling the constitutive relations for finite deformations in continuum me- chanics.
文摘The differences between finite deformation and infinitesimal deformation are discussed. They are exercised on elasto-viscoplastic constitutive relations of concrete. Then, a rate-dependent mechanics model was presented on the basis of Ottosen's four-parameter yield criterion, where different loading surface transferring laws were taken into account, when material was in hardening stage or in softening stage, respectively. The model is well established, so that it can be applied to simulate the response of concrete subject to impact loading. Green-Naghdi stress rate was introduced as objective stress rate. Appropriate hypothesis was postulated in accordance with many experimental results, which could reflect the mechanical behaviour of concrete with large deformation. Available thoughts as well as effective methods are also provided for the research on related engineering problems.
基金Project supported by the National Natural Science Foundation of China (No.10472076)the Natural Science Foundation of Shanxi Province of China (No.2006021005)
文摘A new nonlinear wave equation of a finite deformation elastic circular rod simultaneously introducing transverse inertia and shearing strain was derived by means of Hamilton principle. The nonlinear equation includes two nonlinear terms caused by finite deformation and double geometric dispersion effects caused by transverse inertia and transverse shearing strain. Nonlinear wave equation and corresponding truncated nonlinear wave equation were solved by the hyperbolic secant function finite expansion method. The solitary wave solutions of these nonlinear equations were obtained. The necessary condition of these solutions existence was given also.
文摘Whether the concept of effective stress and strain in elastic-plastic theory is still valid under the condition of finite deformation was mainly discussed. The uni-axial compression experiments in plane stress and plane strain states were chosen for study. In the two kinds of stress states, the stress-strain curve described by logarithm strain and rotated Kirchhoff stress matches the experiments data better than the curves defined by other stress-strain description.
基金supported by the Key Project of the National Natural Science Foundation of China(10932003)Project of Chinese National Programs for Fundamental Research and Development(2012CB619603 and 2010CB832700)"04" Great Project of Ministry of Industrialization and Information of China (2011ZX04001-21)
文摘An algorithm for integrating the constitutive equations in thermal framework is presented, in which the plastic deformation gradient is chosen as the integration variable. Compared with the classic algorithm, a key feature of this new approach is that it can describe the finite deformation of crystals under thermal conditions. The obtained plastic deformation gradient contains not only plastic defor- mation but also thermal effects. The governing equation for the plastic deformation gradient is obtained based on ther- mal multiplicative decomposition of the total deformation gradient. An implicit method is used to integrate this evo- lution equation to ensure stability. Single crystal 1 100 aluminum is investigated to demonstrate practical applications of the model. The effects of anisotropic properties, time step, strain rate and temperature are calculated using this integration model.
文摘By combining grain boundary (GB) and its influence zone, a micromechanic model for polycrystal is established for considering the influence of GB. By using the crystal plasticity theory and the finite element method for finite deformation, numerical simulation is carried out by the model. Calculated results display the microscopic characteristic of deformation fields of grains and are in qualitative agreement with experimental results.
文摘This paper concerns the dynamic plastic response of a circular plate resting on fluid subjected to a uniformly distributed rectangular load pulse with finite deformation. It is assumed that the fluid is incompressible and inviscous, and the plate is made of rigid-plastic material and simply supported along its edge. By using the method of the Hankel integral transformation, the nonuniform fluid resistance is derived as the plate and the fluid is coupled. Finally, an analytic solution for a circular plate under a medium load is obtained according to the equations of motion of the plate with finite deformation.
文摘By using the logarithmic strain, the finite deformation plastic theory, corresponding to the infinitesimal plastic theory, is established successively. The plastic consistent algorithm with first order accuracy for the finite element method (FEM) is developed. Numerical examples are presented to illustrate the validity of the theory and effectiveness of the algorithm.
