Understanding the First Order Inhomogeneous Linear Elasticity through Local Gauge Transformations

TL;DR

This paper investigates the form-invariance of linear elasticity equations under local gauge transformations to clarify different formulations for inhomogeneous media, emphasizing the importance of gauge choices for simplifying calculations.

Contribution

It provides a gauge-theoretic framework to unify various forms of inhomogeneous elasticity equations and guides the selection of physically meaningful gauges.

Findings

Different forms of elasticity equations correspond to different gauge choices.

Choosing appropriate gauges simplifies the mathematical treatment of inhomogeneous media.

The gauge perspective clarifies the intrinsic inhomogeneity effects in elasticity.

Abstract

It is well-known that classical linear elasticity equations are not form-invariant under local transformations. This is intrinsically related to the inhomogeneity of elastic media. However, the reported new linear elasticity equations for inhomogeneous media may appear in different forms. This paper tries to clarify this issue by investigating the form-invariance of the Lagrangian under local temporal or spatial gauge transformations. In this way, these new equations in different forms can be easily understood as the results from different choices of gauge fixing schemes. It recommends to choose appropriate gauges with clear physical meanings to simplify calculations.