The purpose of this chapter is to give a brief introduction to this subject, its basic concepts and theoretical principles for the study of phenomena of electromagneto thermoelastic interaction in material solids. The basic principles presented here are not only valid for conventional electromagnetic solids but also for superconductors. Particular emphasis will be put on electro- and magneto-quasistatic problems which are of practical interest for many engineering applications of electromagnetic mechanical devices involving velocities small compared to the velocity of light. Starting from elementary knowledge of classical electrodynamics and continuum mechanics, the subject will be presented systematically and concisely in a way that both electrical and mechanical engineers who have just begun this subject may benefit and can get a quick and global view about this seemingly complicated subject of electromagnetic-mechanical interaction in material solids. Illustratively, several simplified material models are formulated for some materials as thermoelastic conductors, thermopiezoelectric insulators, soft ferromagnetic elastic insulators, and soft ferromagnetic thermoelastic conductors, which are useful for solving a variety of engineering problems of practical interest.

This chapter reports on the introduction of some theoretical models developed for the study of the electromagneto-mechanical interactions in superconducting materials like RBa₂Cu₃O_x (R=Yb, Gd, Er and Yb). Elasticity (e.g. elastic deformation, Poisson ratio), elastic stress-strain relations, superconducting transition temperature, thermodynamic upper critical field, coherence length, ferromagnetism of magnetic superconductors, saturation magnetization and magnetoelastic superconductors are also reported and considered.