Abstract
In recent years, potential applications have brought about a renewed interest in material with voids. Principally these applications arise in situations where the medium has porosity, rock and soil, bone, and manufactured porous materials. The behavior of granular and porous solids can be analyzed with this theory. This chapter introduces the semi-inverse method applied to the search for variational formulae directly from the field equations and boundary conditions. A family of variational principles for thermo-elasticity with voids is deduced systematically without using the Lagrange multiplier method. The rapid development of computer science and the finite-element applications reveal the importance of searching for a classical variational principle for the discussed problem, which is the theoretical basis of the finite-element methods. Furthermore, such variational formulations have served as a basis for development of a variety of approximate methods of analysis. Recent research reveals that variational theory is also a powerful tool for the mesh-less method or the element-free method.
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