The relations between various couple stress tensors and their change rates are derived. The equations of angular momentum and the corresponding boundary conditions of incremental rate type are presented. Thus the equa...The relations between various couple stress tensors and their change rates are derived. The equations of angular momentum and the corresponding boundary conditions of incremental rate type are presented. Thus the equations of motion and the boundary conditions of incremental rate type of Cauchy form, Piola form and Kirchhoff from for polar continua are obtained in combination of these results with those for classical continuum mechanics derived by kuang Zhenbang.展开更多
Problems of micropolar thermoelasticity have been presented and discussed by some authors in the traditional framework of micropolar continuum field theory. In this paper the theory of micropolar thermoelasticity is r...Problems of micropolar thermoelasticity have been presented and discussed by some authors in the traditional framework of micropolar continuum field theory. In this paper the theory of micropolar thermoelasticity is restudied. The reason why it was restricted to a linear one is analyzed. The rather general principle of virtual work and the new formulation for the virtual work of internal forces as well as the rather complete Hamilton principle in micropolar thermoelasticity are established. From this new Hamilton principle not only the equations of motion, the balance equation of entropy, the boundary conditions of stress, couple stress and heat, but also the boundary conditions of displacement, microrotation and temperature are simultaneously derived.展开更多
In this paper the concrete forms o f dyn amical equations for finite deformable polar elastic media of Boussinesq type, K irchhoff type, Signorini type and Novozhilov type with the help of the anholono mic physical f...In this paper the concrete forms o f dyn amical equations for finite deformable polar elastic media of Boussinesq type, K irchhoff type, Signorini type and Novozhilov type with the help of the anholono mic physical frame method are derived.展开更多
Existing fundamental laws, balance equations and Clausius-Duhem inequalities in continua with microstructure are systematically restudied, and the incomplete formulations of conservation laws of energy and related C-D...Existing fundamental laws, balance equations and Clausius-Duhem inequalities in continua with microstructure are systematically restudied, and the incomplete formulations of conservation laws of energy and related C-D inequalities are pointed out. Some remarks on existing results are made, and new conservation laws of energy and related C-D inequalities are presented.展开更多
A topology optimization method from truss-like continua to perforated continua is studied, which is based on the concept of force transmission paths. The force transmission paths are optimized utilizing a truss-like m...A topology optimization method from truss-like continua to perforated continua is studied, which is based on the concept of force transmission paths. The force transmission paths are optimized utilizing a truss-like material model. In the optimization procedure, parts of the force transmission paths are removed. Finally, perforated optimal continua are formed by further optimizing the material distribution field. No intermediate densities are suppressed; therefore, no additional technique is involved and no numerical instabilities are created. Structural topologies are presented using material distribution fields rather than the ＇existence＇ or ＇inexistence＇ of elements. More detailed structures are obtained utilizing less dense elements.展开更多
This paper considers conservation and balance laws and the constitutive theories for non-classical viscous fluent continua without memory, in which internal rotation rates due to the velocity gradient tensor are incor...This paper considers conservation and balance laws and the constitutive theories for non-classical viscous fluent continua without memory, in which internal rotation rates due to the velocity gradient tensor are incorporated in the thermodynamic framework. The constitutive theories for the deviatoric part of the symmetric Cauchy stress tensor and the Cauchy moment tensor are derived based on integrity. The constitutive theories for the Cauchy moment tensor are considered when the balance of moments of moments 1) is not a balance law and 2) is a balance law. The constitutive theory for heat vector based on integrity is also considered. Restrictions on the material coefficients in the constitutive theories for the stress tensor, moment tensor, and heat vector are established using the conditions resulting from the entropy inequality, keeping in mind that the constitutive theories derived here based on integrity are in fact nonlinear constitutive theories. It is shown that in the case of the simplest linear constitutive theory for stress tensor used predominantly for compressible viscous fluids, Stokes' hypothesis or Stokes'?assumption has no thermodynamic basis, hence may be viewed incorrect. Thermodynamically consistent derivations of the restrictions on various material coefficients are presented for non-classical as well as classical theories that are applicable to nonlinear constitutive theories, which are inevitable if the constitutive theories are derived based on integrity.展开更多
In this paper, we derive non-classical continuum theory for physics of compressible and incompressible thermoviscous non-classical fluent continua using the conservation and balance laws (CBL) by incorporating additio...In this paper, we derive non-classical continuum theory for physics of compressible and incompressible thermoviscous non-classical fluent continua using the conservation and balance laws (CBL) by incorporating additional physics of internal rotation rates arising from the velocity gradient tensor as well as their time varying rates and the rotational inertial effects. In this non-classical continuum theory time dependent deformation of fluent continua results in time varying rotation rates i.e., angular velocities and angular accelerations at material points. Resistance offered to these by deforming fluent continua results in additional moments, angular momenta and inertial effects due to rotation rates i.e., angular velocities and angular accelerations at the material points. Currently, this physics due to internal rotation rates and inertial effects is neither considered in classical continuum mechanics (CCM) nor in non-classical continuum mechanics (NCCM). In this paper, we present a derivation of conservation and balance laws in Eulerian description: conservation of mass (CM), balance of linear momenta (BLM), balance of angular momenta (BAM), balance of moment of moments (BMM), first and second laws of thermodynamics (FLT, SLT) that include: (i) Physics of internal rotation rates resulting from the velocity gradient tensor;(ii) New physics resulting due to angular velocities and angular accelerations due to spatially varying and time dependent rotation rates. The balance laws derived here are compared with those that only consider the rotational rates but neglect rotational inertial effects and angular accelerations to demonstrate the influence of the new physics. Constitutive variables and their argument tensors are established using conjugate pairs in the entropy inequality, additional desired physics and principle of equipresence when appropriate. Constitutive theories are derived using Helmholtz free energy density as well as representation theorem and integrity (complete basis). It is shown that the mathematical model consisting of the conservation and balance laws and constitutive theories presented in this paper has closure. Influence of new physics in the conservation and balance laws on compressible and incompressible thermoviscous fluent continua is demonstrated due to presence of angular velocities and angular accelerations arising from time varying rotation rates when the deforming fluent continua offer rotational inertial resistance. The fluent continua are considered homogeneous and isotropic. Model problem studies are considered in a follow-up paper.展开更多
Three systems of balance equations and jump conditions as well as generalized Clausius\|Duhem inequalities for nonlocal polar thermomechanical continua are naturally and systematically derived under the consideration ...Three systems of balance equations and jump conditions as well as generalized Clausius\|Duhem inequalities for nonlocal polar thermomechanical continua are naturally and systematically derived under the consideration of Euler angles as angular coordinates and the negligence of conservation law of microinertia as well as the introduction of some new definitions. These results are more general than those balance equations and jump conditions as well as generalized Clausius\|Duhem inequalities proposed by Eringen for nonlocal micropolar thermomechanical continua and more suitable to treat the problems of finite deformations.展开更多
From January 1 to March 30, 2008,Continua Beijing will host a solo exhibition of Italian contem- porary art master Michelangelo Pistoletto for the first time. Born in 1933,Michelangelo Pistoletto hehl his first solo e...From January 1 to March 30, 2008,Continua Beijing will host a solo exhibition of Italian contem- porary art master Michelangelo Pistoletto for the first time. Born in 1933,Michelangelo Pistoletto hehl his first solo exhi- hition in Dulin,Italy,and created a series of artworks named after painted objects.These展开更多
Some consistency problems existing in continuum field theories are briefly reviewed. Three arts of consistency problems are clarified based on the renewed basic laws for polar continua. The first art discusses the con...Some consistency problems existing in continuum field theories are briefly reviewed. Three arts of consistency problems are clarified based on the renewed basic laws for polar continua. The first art discusses the consistency problems between the basic laws for polar continua. The second art discusses the consistency problems between the basic laws for polar continua and for other nonpolar continua. The third art discusses the consistency problems between the basic laws for micropolar continuum theories and the dynamical equations for rigid body. The results presented here can help us to get a deeper understanding the structure of the basic laws for various continuum theories and the interrelations between them. In the meantime, these results obtained show clearly that the consistency problems could not be solved in the framework of traditional basic laws for continuum field theories.展开更多
The therrno-mechanical balance equations for a porous material with big irregular pores are derived from the general ones for a medium with ellipsoidal microstructure by imposing the kinematical constraint of micro-st...The therrno-mechanical balance equations for a porous material with big irregular pores are derived from the general ones for a medium with ellipsoidal microstructure by imposing the kinematical constraint of micro-stretch bounded to the macro-deformation： in this case the microstructure disappears apparently （it becomes latent） and the response of the material involves higher gradients of the displacement without incurring known constitutive inconsistencies.展开更多
文摘The relations between various couple stress tensors and their change rates are derived. The equations of angular momentum and the corresponding boundary conditions of incremental rate type are presented. Thus the equations of motion and the boundary conditions of incremental rate type of Cauchy form, Piola form and Kirchhoff from for polar continua are obtained in combination of these results with those for classical continuum mechanics derived by kuang Zhenbang.
文摘Problems of micropolar thermoelasticity have been presented and discussed by some authors in the traditional framework of micropolar continuum field theory. In this paper the theory of micropolar thermoelasticity is restudied. The reason why it was restricted to a linear one is analyzed. The rather general principle of virtual work and the new formulation for the virtual work of internal forces as well as the rather complete Hamilton principle in micropolar thermoelasticity are established. From this new Hamilton principle not only the equations of motion, the balance equation of entropy, the boundary conditions of stress, couple stress and heat, but also the boundary conditions of displacement, microrotation and temperature are simultaneously derived.
文摘In this paper the concrete forms o f dyn amical equations for finite deformable polar elastic media of Boussinesq type, K irchhoff type, Signorini type and Novozhilov type with the help of the anholono mic physical frame method are derived.
文摘Existing fundamental laws, balance equations and Clausius-Duhem inequalities in continua with microstructure are systematically restudied, and the incomplete formulations of conservation laws of energy and related C-D inequalities are pointed out. Some remarks on existing results are made, and new conservation laws of energy and related C-D inequalities are presented.
基金financially supported by the National Natural Science Foundation of China (No. 11572131)
文摘A topology optimization method from truss-like continua to perforated continua is studied, which is based on the concept of force transmission paths. The force transmission paths are optimized utilizing a truss-like material model. In the optimization procedure, parts of the force transmission paths are removed. Finally, perforated optimal continua are formed by further optimizing the material distribution field. No intermediate densities are suppressed; therefore, no additional technique is involved and no numerical instabilities are created. Structural topologies are presented using material distribution fields rather than the ＇existence＇ or ＇inexistence＇ of elements. More detailed structures are obtained utilizing less dense elements.
文摘This paper considers conservation and balance laws and the constitutive theories for non-classical viscous fluent continua without memory, in which internal rotation rates due to the velocity gradient tensor are incorporated in the thermodynamic framework. The constitutive theories for the deviatoric part of the symmetric Cauchy stress tensor and the Cauchy moment tensor are derived based on integrity. The constitutive theories for the Cauchy moment tensor are considered when the balance of moments of moments 1) is not a balance law and 2) is a balance law. The constitutive theory for heat vector based on integrity is also considered. Restrictions on the material coefficients in the constitutive theories for the stress tensor, moment tensor, and heat vector are established using the conditions resulting from the entropy inequality, keeping in mind that the constitutive theories derived here based on integrity are in fact nonlinear constitutive theories. It is shown that in the case of the simplest linear constitutive theory for stress tensor used predominantly for compressible viscous fluids, Stokes' hypothesis or Stokes'?assumption has no thermodynamic basis, hence may be viewed incorrect. Thermodynamically consistent derivations of the restrictions on various material coefficients are presented for non-classical as well as classical theories that are applicable to nonlinear constitutive theories, which are inevitable if the constitutive theories are derived based on integrity.
文摘In this paper, we derive non-classical continuum theory for physics of compressible and incompressible thermoviscous non-classical fluent continua using the conservation and balance laws (CBL) by incorporating additional physics of internal rotation rates arising from the velocity gradient tensor as well as their time varying rates and the rotational inertial effects. In this non-classical continuum theory time dependent deformation of fluent continua results in time varying rotation rates i.e., angular velocities and angular accelerations at material points. Resistance offered to these by deforming fluent continua results in additional moments, angular momenta and inertial effects due to rotation rates i.e., angular velocities and angular accelerations at the material points. Currently, this physics due to internal rotation rates and inertial effects is neither considered in classical continuum mechanics (CCM) nor in non-classical continuum mechanics (NCCM). In this paper, we present a derivation of conservation and balance laws in Eulerian description: conservation of mass (CM), balance of linear momenta (BLM), balance of angular momenta (BAM), balance of moment of moments (BMM), first and second laws of thermodynamics (FLT, SLT) that include: (i) Physics of internal rotation rates resulting from the velocity gradient tensor;(ii) New physics resulting due to angular velocities and angular accelerations due to spatially varying and time dependent rotation rates. The balance laws derived here are compared with those that only consider the rotational rates but neglect rotational inertial effects and angular accelerations to demonstrate the influence of the new physics. Constitutive variables and their argument tensors are established using conjugate pairs in the entropy inequality, additional desired physics and principle of equipresence when appropriate. Constitutive theories are derived using Helmholtz free energy density as well as representation theorem and integrity (complete basis). It is shown that the mathematical model consisting of the conservation and balance laws and constitutive theories presented in this paper has closure. Influence of new physics in the conservation and balance laws on compressible and incompressible thermoviscous fluent continua is demonstrated due to presence of angular velocities and angular accelerations arising from time varying rotation rates when the deforming fluent continua offer rotational inertial resistance. The fluent continua are considered homogeneous and isotropic. Model problem studies are considered in a follow-up paper.
文摘Three systems of balance equations and jump conditions as well as generalized Clausius\|Duhem inequalities for nonlocal polar thermomechanical continua are naturally and systematically derived under the consideration of Euler angles as angular coordinates and the negligence of conservation law of microinertia as well as the introduction of some new definitions. These results are more general than those balance equations and jump conditions as well as generalized Clausius\|Duhem inequalities proposed by Eringen for nonlocal micropolar thermomechanical continua and more suitable to treat the problems of finite deformations.
文摘From January 1 to March 30, 2008,Continua Beijing will host a solo exhibition of Italian contem- porary art master Michelangelo Pistoletto for the first time. Born in 1933,Michelangelo Pistoletto hehl his first solo exhi- hition in Dulin,Italy,and created a series of artworks named after painted objects.These
基金Project supported by the National Natural Science Foundation of China(No.10472041)
文摘Some consistency problems existing in continuum field theories are briefly reviewed. Three arts of consistency problems are clarified based on the renewed basic laws for polar continua. The first art discusses the consistency problems between the basic laws for polar continua. The second art discusses the consistency problems between the basic laws for polar continua and for other nonpolar continua. The third art discusses the consistency problems between the basic laws for micropolar continuum theories and the dynamical equations for rigid body. The results presented here can help us to get a deeper understanding the structure of the basic laws for various continuum theories and the interrelations between them. In the meantime, these results obtained show clearly that the consistency problems could not be solved in the framework of traditional basic laws for continuum field theories.
文摘The therrno-mechanical balance equations for a porous material with big irregular pores are derived from the general ones for a medium with ellipsoidal microstructure by imposing the kinematical constraint of micro-stretch bounded to the macro-deformation： in this case the microstructure disappears apparently （it becomes latent） and the response of the material involves higher gradients of the displacement without incurring known constitutive inconsistencies.
