On the Coupling Effects between Elastic and Electromagnetic Fields from the Perspective of Conservation of Energy

TL;DR

This paper analyzes the energy conservation principles in elastic-electromagnetic coupling effects, revealing how energy conversion occurs in different physical phenomena and clarifying the underlying mechanisms through an energy-based perspective.

Contribution

It provides a comprehensive energy-based analysis of elastic-electromagnetic coupling effects, highlighting the mechanisms of energy conversion and clarifying the roles of work terms and electromagnetic contributions.

Findings

Energy is conserved in piezoelectric and piezomagnetic effects via work terms.

Electromagnetic energy contributes to elastic energy in Villari effects.

Electrostriction and magnetostriction are driven by Maxwell stress with purely electromagnetic energy.

Abstract

Coupling effects among different physical fields substantially reflect the conversion of energies from one form into another. For simple physical processes, their governing or constitutive equations all satisfy the law of conservation of energy. Then, analysis is extended to coupling effects. First, it is found for the linear direct and converse piezoelectric and piezomagnetic effects, their constitutive equations guarantee that the total energy is conserved during the process of energy conversion between the elastic and electromagnetic fields; however, energies are converted via work terms, $(\beta_{ijk} E_i )_{,k} v_j$ and $(\gamma_{ijk} H_i)_{,k} v_j$, rather than via energy terms, $\beta_{ijk} E_i e_{jk}$ and $\gamma_{ijk} H_i e_{jk}$. Second, for the generalized Villari effects, the electromagnetic energy can be treated as an extra contribution to the generalized elastic energy. Third, for electrostriction and magnetostriction, it is argued both effects are induced by the Maxwell stress; moreover, their energy is purely electromagnetic and thus both have no converse effects. During these processes, energy can be converted in three different ways, i.e., via non-potential forces, via cross-dependence of energy terms and directly via the electromagnetic interactions of ions and electrons. In the end, general coupling processes which involve elastic, electromagnetic fields and diffusion are also analyzed. The advantage of using this energy formulation is that it facilitates discussions of the conversion of energies and provides better physical insights into the mechanisms of these coupling effects.