Fundamentals of magneto-electro-mechanical couplings: Continuum formulations and invariant requirements

Abstract

Couplings of magnetic and electric fields in materials could allow for promising applications in medical and information technology. In this contribution, we recapitulate well-known aspects of magneto-electro-mechanical properties and their couplings. At first, we echo basic aspects of electricity and magnetism and Maxwell’s equations. Secondly, we summarize the governing equations for electrostatics and magnetostatics, point out the properties of physical fields across internal surfaces, and discuss the work-energy theorem of electrodynamics, the so-called Poynting‘s theorem. Thirdly, we will discuss some fundamental concepts of magneto-electro-mechanical couplings in matter. Here, we will formulate thermodynamic potentials depending on different basic variables in order to be flexible with a view to different modeling aspects. Afterwards, we discuss aspects of form-invariance of physical laws under coordinate transformations: Lorentz invariance, Galilean transformation and time reversal. Here, we focus on piezoelectric as well as on magnetic symmetry groups and give remarks on classical invariant theory suitable for coordinate-invariant modeling of thermodynamical potentials.