Hyperbolic theories and problems of continuum mechanics

Theories and problems of that part of continuum thermomechanics which can not be properly formulated without partial differential equations of hyperbolic analytical type are considered. Special attention is paid to comparatively new hyperbolic continuum theories: the theory of three-dimensional perfect plasticity and the theory of micropolar thermoelasticity. The latter is accepted as type-II thermoelasticity. Three-dimensional statical and kinematical equations of the perfect plasticity theory by Ishlinskii and Ivlev are studied in order to elucidate their analytical type and opportunity to obtain integrable equations along some special lines. A new approach to hyperbolic formulations of thermoelasticity presumes consideration of referential gradients of thermodynamic state variables and extra field variables (rapid variables) as independent functional arguments in the action density. New hyperbolic thermomechanics of micropolar thermoelastic media is developed within the framework of classical field theory by the variational action integral and the least action principle.

continuum, hyperbolicity, perfect plasticity, thermoelasticity, action, least action principle