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

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.

arXiv comment30 pages, 1 figure

References in corpus (12)

• Historical roots of gauge invariance
• Overall Dynamic Properties of 3-D periodic elastic composites
• Minimum dissipation principle in stationary non equilibrium states
• Nonlinear and Linear Elastodynamics Transformation Cloaking
• Realizing the Willis equations with pre-stresses
• On the Jacobi metric for a general Lagrangian system
• The form-invariance of wave equations without requiring a priori relations between field variables
• An experimental verification of the one-dimensional static Willis-form equations
• Performance Assessment of Energy-preserving, Adaptive Time-step Variational Integrators
• Emmy Noether on Energy Conservation in General Relativity
• Modified 1D elastic wave equations that retain time synchronization under spatial coordinate transformations
• Understanding the First Order Inhomogeneous Linear Elasticity through Local Gauge Transformations