%0 Journal Article
%T Finite Deformation, Finite Strain Nonlinear Micropolar NCCT for Thermoviscoelastic Solids with Rheology
%A Karan S. Surana
%A Sri Sai Charan Mathi
%J Applied Mathematics
%P 143-168
%@ 2152-7393
%D 2025
%I Scientific Research Publishing
%R 10.4236/am.2025.161006
%X 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 <math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'>
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 and 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&#8217;s strain rates up to order <math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'>
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; 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 <math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'>
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) tensor up to order <math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'>
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, 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 <math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'>
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, 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 <math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'>
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, 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
%K Nonclassical
%K Micropolar
%K Dissipation
%K Ordered Rate
%K Conservation and Balance Laws
%K Representation Theorem
%K Microviscous Dissipation
%K Microdissipation
%K Ordered Rate
%K Finite Deformation Theories
%K Finite Strain
%K Conservation and Balance Laws
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=140330