Cauchy-Maxwell equations: A unified field theory for coupled electromagnetism and elasticity

• Main Authors: Roy, Pranesh, Kumar, Sanjeev, Roy, Debasish
• Format: Journal Article
• Language: English
• Published: 19-11-2019
• Subjects: Physics - Classical Physics; Physics - Computational Physics
• DOI: 10.48550/arxiv.2001.02537

A conformal gauge theory is used to describe and unify myriad
electromechanical and magnetomechanical coupling effects observed in solid
continua. Using a space-time pseudo-Riemannian metric in a finite-deformation
setup and exploiting the local conformal symmetry of the Lagrangian, we derive
Cauchy-Maxwell (CM) equations that seamlessly combine, for the first time,
Cauchy's elasto-dynamic equations with Maxwell's equations for
electromagnetism. Maxwell's equations for vacuum are recoverable from our
model, which in itself also constitutes a new derivation of these equations.
With deformation gradient and material velocity coupled in the Lagrange
density, various pseudo-forces appear in the Euler-Lagrange equations. These
forces, not identifiable through classical continuum mechanics, may have
significance under specific geometric or loading conditions. As a limited
illustration on how the CM equations work, we carry out semi-analytical
studies, viz. on an infinite body subject to isochoric deformation and a finite
membrane under both tensile and transverse loading, considering
piezoelectricity and piezomagnetism. Our results show that under specific
loading frequencies and tension, electric and magnetic potentials may increase
rapidly in some regions of the membrane. This may have significance in future
studies on efficient energy harvesting.