Generalized variational principle of an elastic body with voids and their applications

Based on the linear theory of elasticity, a constitutive model of generalized force fields for elastic solid with voids was constructed. By using the variational integral method, the generalized variational principle and the potential energy principle of elastic solids with voids were presented. It can be shown that the variational principle yields the governing differential equations and the corresponding initial and boundary conditions of elastic body with voids. As an application, a generalized variational approach for elastic Timoshenko beams with damage was obtained. The variational principle provides an effective way for solving problems of elastic solids with voids.