Deeper understandings of the gauge theory for the first order inhomogeneous linear elasticity

TL;DR

This paper advances the gauge theory framework for inhomogeneous linear elasticity by integrating temporal and spatial transformations, ensuring thermodynamic consistency and capturing thermal stresses.

Contribution

It introduces generalized equations that unify temporal-spatial transformations and adhere to thermodynamic laws, improving the modeling of inhomogeneous elastic media.

Findings

Derived equations are consistent with thermodynamics.

The framework captures thermal stresses.

The approach distinguishes dissipative and non-dissipative energies.

Abstract

Our previous study [1] has demonstrated that the gauge theory is a proper framework for characterizing the local temporal and spatial interactions in inhomogeneous elastic media. However, in that study temporal interactions were interpreted as the compensation for the loss of kinetic energy resulting from homogenization process, distinct from damping effects. In addition, that study did not account for the integration of temporal and spatial transformations, leading to the omission of some crucial information such as thermal stresses. In this paper, we address this oversight to establish generalized equations by employing a unified methodology that encompasses the integrated temporal-spatial transformations and the principle of minimum dissipation. Among many interesting new findings, we highlight that the newly derived equations are inherently consistent with the first and the second laws of thermodynamics, because this gauge theory naturally incorporates the fundamental mechanism that governs the partitioning between the dissipative and the non-dissipative energy.