TITLE:
A Linear Microdilation Microcontinuum Theory for Thermoelastic Solids
AUTHORS:
Karan S. Surana, Michael Poskin
KEYWORDS:
Microstretch Microvolumetric Micro, Macro Integral-Average Representation Theorem Balance of Moment of Moments Thermolelastic Conservation and Balance Laws Constitutive Theories
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.13 No.11,
November
21,
2025
ABSTRACT: 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.