Book Description

This paper studies the steady-state behavior of solids that can sustain mechanical, electromagnetic, and thermal effects. The authors examine a class of boundary-value problems for a quasilinear system of functional differential equations that is derived from a very general model for such materials. They propose a physically reasonable constitutive theory which leaves this system amenable to modern methods of partial differential equations. The principal assumption is a modified version of the strong ellipticity condition. Part I proves existence results for the general system under some special physical assumptions (rigidity and hyperelasticity). The formulation admits non-local interactions caused by the magnetic 'self-field' generated by the deformed, conducting body. Part II shows the existence and regularity of solutions of a system of functional ordinary differential equations arising from a semi-inverse problem in a more comprehensive physical situation. Keywords: Smooth solutions; Polyconvex energy functions; Electro-elastic coupling; Magneto-elastic coupling; Conducting rods; Thermo-elastic coupling. (Author).