Analysis of Effective Properties of Poroelastic Composites with Surface Effects Depending on Boundary Conditions in Homogenization Problems

Abstract

The paper considers the homogenization problems for two-component poroelastic composites with a random structure of nanosized inclusions. The nanoscale nature of the inclusions was taken into account according to the generalized Gurtin–Murdoch theory by specifying surface elastic and porous stresses at the interface boundaries, the scale factor of which was related to the size of the inclusions. The formulation of homogenization problems was based on the theory of effective moduli, considering Hill’s energy relations. The problems of static poroelasticity were solved in accordance with the Biot and filtration models. A feature of this investigation was the comparison of solutions of four types of homogenization problems with different boundary conditions. Modeling of representative volumes and solving problems of determining the effective material moduli were carried out in the ANSYS finite element package. Representative volumes were built in the form of a cubic grid of hexahedral finite elements with poroelastic properties of materials of one of the two phases and with a random arrangement of elements of the second phase. To consider interface effects, the interfaces were covered with shell elements with options for membrane stresses. The results of computational experiments made it possible to study the effective moduli depending on the boundary conditions, on the percentage of inclusions, their characteristic nanosizes, and areas of interface boundaries.