The basic field equations, boundary conditions, and constitutive equations, necessary for the treatment of problems involving the nonlinear, steady state behaviour of isotropic elastic solids subject to large deformations, electromagnetic fields and thermal gradients, are derived and employed to solve three specific problems. In Part I the basic equations are formulated to include Maxwell's equations, laws of conservation of mass and of energy, and principles of balance of momentum and balance of moment of momentum. The principle of equipresence and the invariance requirements of the theory of continuous media are employed to develop a constitutive theory in which the stress, dielectric displacement, electric current, magnetic flux density, and heat flux are assumed to be analytic tensor point functions of strain, electric field, magnetic field and thermal gradient. The elastic solids so characterized are further restricted by the assumption of hemihedral or holohedral isotropy with respect to mechanical, electrical, magnetic and thermal properties. In Part II (pp. 97–114) are given a number of special theories deducible from the general consitutive equation developed in Part I, e.g. rigid motion, electroelasticity, and magnetoelasticity. Linear, second degree, and other approximate constitutive equations are also discussed in detail. The problems solved are: Simple shear of an infinite, dielectric slab the faces of which are maintained at different temperatures and potentials; Torsion of an incompressible, circular, conducting cylinder with axial electric field; and Response of a rigid, annular, dielectric cylinder to an axial magnetic field and radial electric field. Part I is made self-contained through the appendices which give the expansion for any symmetric or anti-symmetric 3 × 3 matrix which can be expressed as a polynomial in one symmetric and three anti-symmetric matrices.
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