Generalized plane deformation of electromagnetic thermoelastic solids I. Correspondence and invariance shifts

This two-part paper extends the recent results in plane elasticity to gener alized plane deformation of electromagnetic thermoelastic materials. These include the correspondences between various physical contexts, invariance o f stresses under a change in elastic compliance, and the reduced dependence of effective elastic compliance upon the material constants. The first par t is concerned with the issues of correspondence and invariance shifts. Fur ther results on invariance shifts and reduced independence of effective mod uli are presented in part II. We considered a cylindrical body in which the cross-sections and material moduli do not vary with the axial direction. T he loading and geometric configurations are arranged so that the stress, el ectric displacement and magnetic induction fields are independent of the ax ial direction. A general solution framework is outlined. With the help of s ome tensor notations together with proper arrangements of the constitutive equations, the field equations of deformation of this kind are written in a compact form. The relationships between various field variables are then e asily identified. This permits us to reconstruct the correspondence relatio ns between various systems in a broader sense under all kinds of crystallog raphic and non-crystallographic point-group symmetry. Complete forms of inv ariance shifts of moduli together with a proof of the completeness are give n. This provides some new insights of the original discovery by Cherkaev, L urie & Milton.