Incompatible deformations in solids subjected to coupled thermal and electromagnetic fields

The purpose of this study is to develop a theory of incompatible deformations and evolutionary problems for thermoelastic-electromagnetic solids. The complexity of the problem under consideration lies in the fact that, although the theory of electromagnetism is quite fully developed, it is abstracted from specific materials. On the other hand, issues related to materials and wave propagation in media are primarily associated with polarization, and very few studies exist that consider the mutual influence of mechanical, electromagnetic, and, especially, temperature fields. This influence is primarily considered for piezoelastic materials, since the latter have been used since the time of the Curie brothers as elements of scales, gyroscopes, etc. In addition, piezoresistive materials are considered. However, all of these are special cases that do not encompass the general theory. This is precisely why this study is relevant. Despite the complex interaction between temperature and electromagnetic fields, it remains possible to use differential geometry methods to model incompatible deformations. This paper proposes a local discharging hypothesis, which intuitively generalizes a thought experiment involving dividing a self-stressed body into infinitesimal parts. These parts then unload independently to a stress-free state. The globally self-stressed state is modeled using Weitzenb¨ock space (a space with nonvanishing torsion). An evolution equation is proposed that characterizes the relationship between the rate of change of the torsion (or, equivalently, dislocation density tensor) and the action of temperature and electromagnetic fields.