Three-Dimensional Model for a Porous Elastic Anisotropic Solid with Inclusions, Taking into Account Dissipation, Heat Flux, Radiation and Thermal Stress

摘要

A number of applications arise where a porous solid body with inclusions is subjected to large stresses and the influence of heat transfer, both by conduction and by radiation. Often, such a body is anisotropic either because of its method of manufacture, or in the case of geological materials, because of its method of formation. Though a priori, empirical, and semi-empirical models and partial models for such materials are commonly used in engineering calculations, no three-dimensional model exists which takes all of these phenomena into account, and also has been shown to be in accord with all of the accepted principles for formulating constitutive equations. The basic principles we use are straightforward applications of techniques of rational mechanics, most developed many years ago, but some settled only quite recently, and principally as a result of research done at Sandia National Laboratories. Since the problem we consider is intrinsically complicated, it is no surprise that the equations are complicated also. However, we do attempt to formulate the model with the greatest economy of formalism consistent with our goals. Since we are dealing with a material composed of more than one constituent, we use a mixture theory. The constituent of primary interest is a porous hyperelastic solid, which we allow to undergo finite deformations. The other constituent is a dissipative material which we envision as filling part of the pore space in the elastic material. The rest of the pore space is treated as vacuous, though we allow for pore crushing through a dissipative mechanism. (ERA citation 09:051061)