This article proposes a simplified way to solve solid mechanic problems in micropolar elasticity using the solution found in the classic theory of elasticity as a starting point. In this study, an analysis of the line...This article proposes a simplified way to solve solid mechanic problems in micropolar elasticity using the solution found in the classic theory of elasticity as a starting point. In this study, an analysis of the linear isotropic micropolar elasticity is conducted based on the properties imposed on the micropolar medium by the constitutive and equilibrium equations. To ascertain how the micropolar medium responses deviate from Hooke’s theory of elasticity, different loading conditions were classified. Three cases have been found so far: the rotational couple response, the quasi-classic equilibrium of momentum response and the general case. This study is the first in a series planned to explore the use of commercial packages of finite element in order to solve micropolar elasticity problems.展开更多
In this paper,we consider the derivation of constitutive theories for a linear micromorphic polymeric solid medium in which the microconstituents,the solid medium and the interaction of the microconstituents with the ...In this paper,we consider the derivation of constitutive theories for a linear micromorphic polymeric solid medium in which the microconstituents,the solid medium and the interaction of the microconstituents with the solid medium have mechanisms of elasticity,dissipation and rheology.Thermodynamically and mathematically consistent conservation and balance laws derived by Surana et al.in a recent paper for linear micromorphic solids are utilized in the present work.The conjugate pairs in the entropy inequality,in conjunction with the axiom of causality,are used in establishing constitutive tensors and the initial choice of argument tensors.These are modified or augmented to incorporate a more comprehensive ordered rate mechanism of dissipation and rheology for the microconstituents,the medium,and the interaction of the microconstituents with the solid medium.The constitutive theories presented in the paper provide spectra of viscosities and relaxation times.Constitutive theories and the material coefficients are derived using the representation theorem based on integrity.Simplified forms of the constitutive theories are also presented.It is shown that the complete mathematical model,consisting of the conservation and balance laws and the constitutive theories,has closure without the use of the conservation of microinertia law advocated and used by Eringen and another additional balance law also used by Eringen to obtain six equations needed for closure;both of these laws are outside the thermodynamic framework.展开更多
文摘This article proposes a simplified way to solve solid mechanic problems in micropolar elasticity using the solution found in the classic theory of elasticity as a starting point. In this study, an analysis of the linear isotropic micropolar elasticity is conducted based on the properties imposed on the micropolar medium by the constitutive and equilibrium equations. To ascertain how the micropolar medium responses deviate from Hooke’s theory of elasticity, different loading conditions were classified. Three cases have been found so far: the rotational couple response, the quasi-classic equilibrium of momentum response and the general case. This study is the first in a series planned to explore the use of commercial packages of finite element in order to solve micropolar elasticity problems.
文摘In this paper,we consider the derivation of constitutive theories for a linear micromorphic polymeric solid medium in which the microconstituents,the solid medium and the interaction of the microconstituents with the solid medium have mechanisms of elasticity,dissipation and rheology.Thermodynamically and mathematically consistent conservation and balance laws derived by Surana et al.in a recent paper for linear micromorphic solids are utilized in the present work.The conjugate pairs in the entropy inequality,in conjunction with the axiom of causality,are used in establishing constitutive tensors and the initial choice of argument tensors.These are modified or augmented to incorporate a more comprehensive ordered rate mechanism of dissipation and rheology for the microconstituents,the medium,and the interaction of the microconstituents with the solid medium.The constitutive theories presented in the paper provide spectra of viscosities and relaxation times.Constitutive theories and the material coefficients are derived using the representation theorem based on integrity.Simplified forms of the constitutive theories are also presented.It is shown that the complete mathematical model,consisting of the conservation and balance laws and the constitutive theories,has closure without the use of the conservation of microinertia law advocated and used by Eringen and another additional balance law also used by Eringen to obtain six equations needed for closure;both of these laws are outside the thermodynamic framework.
