Calculation of the effective properties of the prestressed nonlinear elastic heterogeneous materials under finite strains based on the solutions of the boundary value problems using finite element method

Abstract

This paper describes the approach and algorithms for numerical estimation of the effective properties of the prestressed nonlinear elastic heterogeneous materials under finite strains. To numerically evaluate effective properties on a representative volume (or periodicity cell), a series of sequences of elasticity problems differing in the type of the applied boundary conditions is solved. In all the problems being solved, along with the specially applied boundary conditions, the model undergoes the same predetermined prestress. In addition, a separate problem is being solved, in which, besides the prestressed state, zero displacement of the model boundary are set. The results of solving each problem in the form of stress tensors are averaged over the volume. Numerical calculations were carried out using the Fidesys Composite software module of the Fidesys CAE system using the finite element method. The paper presents the solution to a number of problems to estimate the effective coefficients of the porous material prestressed by pore pressure. Dependence graphs of effective properties on porosity and on size of pore pressure are constructed.