A simple,efficient and accurate high resolution method to tracking moving-interfaces-the characteristic integral-averaging finite volume method on unstructured meshes is proposed. And some numerical tests and evaluati...A simple,efficient and accurate high resolution method to tracking moving-interfaces-the characteristic integral-averaging finite volume method on unstructured meshes is proposed. And some numerical tests and evaluation of six main efficient methods for interface reconstruction are made. Through strict numerical simulation,their characters,advantages and shortcomings are compared,analyzed and commended in particular.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
This paper presents a linear microdilation microcontinuum theory in which the microconstituents have only one unknown degree of freedom,volumetric strain or a quantity proportional to volumetric strain,and have three ...This paper presents a linear microdilation microcontinuum theory in which the microconstituents have only one unknown degree of freedom,volumetric strain or a quantity proportional to volumetric strain,and have three known rigid rotational degrees of freedom defined by the classical rotations.In this microdilation theory,the microconstituents,the medium as well as the interaction of the microconstituents all have thermoelastic deformation physics.Additionally,the microconstituents can experience rigid rotations.Due to deformable microconstituents,we begin the derivation with the microconstituent conservation and balance laws using classical continuum mechanics,followed by integral-average definitions that facilitate derivation of macro conservation and balance laws.This microdilation theory is completely different than Eringen’s microstretch theory;the differences are discussed in the paper.It is shown that the approach of using smoothing weight functions in deriving macro balance of linear momenta,macro balance of angular momenta and the new balance law proposed for closure of the mathematical model in Eringen’s work is neither needed nor used in the present work and is not supported by thermodynamics.All constitutive theories are derived using representation theorem and integrity,hence mathematically consistent and complete.The linear microdilation theory presented in this paper for thermoelastic solids is shown to be thermodynamically and mathematically consistent.展开更多
This paper presents derivation of micro and macro conservation and balance laws and the constitutive theories for the linear elastic micromorphic theory,in which elasticity is considered for microconstituents,the soli...This paper presents derivation of micro and macro conservation and balance laws and the constitutive theories for the linear elastic micromorphic theory,in which elasticity is considered for microconstituents,the solid medium,and for the interaction of microconstituents with the solid medium.The conservation and balance laws are initiated for micro deformation,followed by consistent“integral-average”definitions valid at the macro level.These permit the derivation of the conservation and balance laws at the macro level.Significant aspects of this theory are:1)microconstituent rigid rotation physics is the same in all 3M theories.The rigid rotations of the microconstituents are in fact classical rotations;hence,they do not introduce three unknown degrees of freedom at the material point and also can not be part of the strain measures.Thus,in this theory,a microconstituent has only six unknown degrees of freedom,six independent components of the symmetric part of the micro deformation gradient tensor,as opposed to Eringen’s theory,in which all nine components of the micro deformation gradient tensor are unknown degrees of freedom.2)The balance of moment of moments balance law is shown to be essential in all 3M theories and hence is considered here,due to which the Cauchy moment tensor is symmetric.This avoids a spurious constitutive theory for the moment tensor.3)In the case of nonsymmetric macro Cauchy stress tensor,the constitutive theory is needed only for the symmetric part,as the skew-symmetric part is defined by the balance of angular momenta.4)The smoothing weighting functionφ^((α))for the microconstituent,as advocated by Eringen and used to multiply the balance of linear momenta of the micro deformation physics,has no thermodynamic,physical or mathematical basis;hence,it is not used in the present work.5)In contrast with published works of Eringen and others,all constitutive tensors of rank two are always symmetric,hence always permitting the use of the representation theorem in deriving constitu tive theories,ensuring the mathematical consistency of the resulting theories.6)Conservation of micro inertia,necessary in Eringen’s theories to provide closure to the mathematical model,is neither needed nor used in the present work.The linear micromorphic theory derived here is compared with Eringen’s theory to identify differences,discuss and evaluate these for their validity based on thermodynamic and mathematical principles to ultimately determine the thermodynamic and mathematical consistency of the published micromorphic theories.展开更多
文摘A simple,efficient and accurate high resolution method to tracking moving-interfaces-the characteristic integral-averaging finite volume method on unstructured meshes is proposed. And some numerical tests and evaluation of six main efficient methods for interface reconstruction are made. Through strict numerical simulation,their characters,advantages and shortcomings are compared,analyzed and commended in particular.
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.
文摘This paper presents a linear microdilation microcontinuum theory in which the microconstituents have only one unknown degree of freedom,volumetric strain or a quantity proportional to volumetric strain,and have three known rigid rotational degrees of freedom defined by the classical rotations.In this microdilation theory,the microconstituents,the medium as well as the interaction of the microconstituents all have thermoelastic deformation physics.Additionally,the microconstituents can experience rigid rotations.Due to deformable microconstituents,we begin the derivation with the microconstituent conservation and balance laws using classical continuum mechanics,followed by integral-average definitions that facilitate derivation of macro conservation and balance laws.This microdilation theory is completely different than Eringen’s microstretch theory;the differences are discussed in the paper.It is shown that the approach of using smoothing weight functions in deriving macro balance of linear momenta,macro balance of angular momenta and the new balance law proposed for closure of the mathematical model in Eringen’s work is neither needed nor used in the present work and is not supported by thermodynamics.All constitutive theories are derived using representation theorem and integrity,hence mathematically consistent and complete.The linear microdilation theory presented in this paper for thermoelastic solids is shown to be thermodynamically and mathematically consistent.
文摘This paper presents derivation of micro and macro conservation and balance laws and the constitutive theories for the linear elastic micromorphic theory,in which elasticity is considered for microconstituents,the solid medium,and for the interaction of microconstituents with the solid medium.The conservation and balance laws are initiated for micro deformation,followed by consistent“integral-average”definitions valid at the macro level.These permit the derivation of the conservation and balance laws at the macro level.Significant aspects of this theory are:1)microconstituent rigid rotation physics is the same in all 3M theories.The rigid rotations of the microconstituents are in fact classical rotations;hence,they do not introduce three unknown degrees of freedom at the material point and also can not be part of the strain measures.Thus,in this theory,a microconstituent has only six unknown degrees of freedom,six independent components of the symmetric part of the micro deformation gradient tensor,as opposed to Eringen’s theory,in which all nine components of the micro deformation gradient tensor are unknown degrees of freedom.2)The balance of moment of moments balance law is shown to be essential in all 3M theories and hence is considered here,due to which the Cauchy moment tensor is symmetric.This avoids a spurious constitutive theory for the moment tensor.3)In the case of nonsymmetric macro Cauchy stress tensor,the constitutive theory is needed only for the symmetric part,as the skew-symmetric part is defined by the balance of angular momenta.4)The smoothing weighting functionφ^((α))for the microconstituent,as advocated by Eringen and used to multiply the balance of linear momenta of the micro deformation physics,has no thermodynamic,physical or mathematical basis;hence,it is not used in the present work.5)In contrast with published works of Eringen and others,all constitutive tensors of rank two are always symmetric,hence always permitting the use of the representation theorem in deriving constitu tive theories,ensuring the mathematical consistency of the resulting theories.6)Conservation of micro inertia,necessary in Eringen’s theories to provide closure to the mathematical model,is neither needed nor used in the present work.The linear micromorphic theory derived here is compared with Eringen’s theory to identify differences,discuss and evaluate these for their validity based on thermodynamic and mathematical principles to ultimately determine the thermodynamic and mathematical consistency of the published micromorphic theories.
