Constitutive Equation of Low-Density Porous Materials Incorporating Structure Transformations Induced by Cellular Crush

Abstract

Low-density porous materials like sponge have various abilities as functional solid in mechanical design. Especially the remarkable nonlinearity in forming process causes difficulty in numerical analysis of the mechanical behavior of the porous materials. In this paper, the nonlinear deformation process of the low-density porous materials is represented by using the constitutive equation incorporating structure transformation. The porous material has the complicated cellular structure mesoscopically, and then two structures can be defined with and without the cellular structure. The structure transformation which loses the cellular causes the volume change. The adopted constitutive equation includes the valuable of volume fraction, but large change of the volume needs the idea of nominal and true volume fraction even if only nominal one is used in the analysis of conventional transformation problems. Two types of low-density porous materials are inspected to verify the ability of the equation. One has reversible character like typical elastic sponge, and the other has irreversible character like expanded polystyrene. The equation is applied to represent the experimental results of compression testing on two materials. Then it is shown that the adopted constitutive equation has the ability to represent the mesoscopical change of the low-density porous materials macroscopically.