Static and dynamic behavior of porous elastic materials based on micro-dilatation theory: A numerical study using the MLPG method

A meshless local Petrov-Galerkin (MLPG) model of porous elastic materials based on micro-dilatation theory by Cowin and Nunziato (1983) is developed. . This theory describes properties of homogeneous elastic materials with voids free of fluid. The primal fields (mechanical displacements, and change in matrix volume fraction which is also called micro-dilatation) are coupled in the constitutive equations. The governing differential equations are satisfied in the weak form on small circular subdomains for 2D problems. Only one node is lying at the center of each subdomain spread on the analyzed domain. A Heaviside step function is applied as test functions in the weak-form to derive local integral equations on subdomains. The spatial variation of the displacements and micro-dilatation are approximated by the moving least-squares (MLS) scheme. After performing the spatial integrations, a system of ordinary differential equations for certain nodal unknowns is obtained.