Evaluation of Effect of Microscopic Structure of Closed-Cell Foam by Homogenization FEM

Abstract

In this study, the effect of microscopic structures of foam rubber were investigated numerically. A 2-dimensional finite element analysis code and a 2-dimentional homogenization finite element analysis code of the hyperelastic material were developed, respectively. The incompressible hyperelasticity in the total Lagrangian finite strain framework was applied to both of the general FEM and the homogenization FEM codes. The reason of which foam rubber were used widely, is that it has some advantage properties. But effect of microscopic structure on macroscopic stress-strain relationships is not evaluated enough in the point of engineering material design. To clear this engineering issue, compression loading tests of rubber specimens which have periodic geometrical holes were conducted to evaluate the effect of periodical structure on mechanical characteristics. Relative density of natural rubber specimens were 42%, 56%, 72%, 80% and 86%, respectively. The biaxial tensile tests of rubber sheets which were made from same natural rubber used in compression loading tests were conducted to identify material coefficients of the elastic potential function of the hyperelastic matrix. The stress-strain relationships given by compression loading tests of the natural rubber specimens were simulated by the finite element analysis programs with the general boundary condition and the periodic boundary condition to investigate the applicability of homogenized method to foam rubber.