Author(s)

Karan S. Surana^1*, Sri Sai Charan Mathi²

¹Department of Mechanical Engineering, University of Kansas, Lawrence, KS, USA.
²Trane Technologies, La Crosse, WI, USA.

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.

Linear Micromorphic, Microcontinuum, Conservation and Balance Laws, Constitutive Theories, Integral-Average, Integrity, Representation Theorem, Dissipation, Memory, Rheology, Polymeric Solid

Surana, K. and Mathi, S. (2025) Constitutive Theories for Linear Micromorphic Polymeric Solids. Journal of Applied Mathematics and Physics, 13, 3739-3764. doi: 10.4236/jamp.2025.1311209.