COMPLEMENTARY VARIATIONAL-PRINCIPLES FOR GENERALIZED DYNAMIC CONTINUUM MODELS

Complementary variational principles are presented for a range of dynamic continuum models based on fully coupled inhomogeneous, anisotropic poroelasticity, extended to include coupled thermal effects and viscoelastic behaviour. The dual principles are all developed in Laplace transform space. Previous results using variational principles to derive bounds on effective permeability for a rigid porous solid for both steady and unsteady loading are generalized to the anisotropic case. As an illustration of the power of the dual principles, bounds are placed on the Stress Intensity Factor for a sample fracture problem in dynamic thermoelasticity, in transform space. Very good bounds are obtained by using an optimization method with the dual principles. Results for a specific inhomogeneous material are shown, and compared with published results in the literature concerning so called Functionally Gradient Materials.