Appropriate modeling of the macroscopic mechanical response of these materials under arbitrarily large deformations is therefore the main requirement for engineering applications.
This document provides a summary of a remarkably simple and accurate constitutive model to describe the macroscopic elastic response of porous elastomers based on homogenization solutions. The model is very suitable for implementation in Abaqus using the UHYPER user subroutine. A schematic of a porous elastomer with spherical pores of monodisperse size is shown in Figure 1.
Figure 1: Schematic of a porous elastomer. (Courtesy of Professor Victor Lefèvre)
To demonstrate the applicability of the homogenization model and the associated UHYPER user subroutine, several examples of industrial interests with relatively simplified geometries are included in the document. For instance, Figure 2 shows the porosity of the material at the beginning (50% initial porosity, f_0=0.5) and the end of the analysis in a simplified automotive boot seal model. This model is modified from Abaqus | Example Problems | Static Stress | Displacement Analyses | Static and quasi-static stress analyses | Analysis of an automotive boot seal of the SIMULIA User Assistance 2019.
Figure 2: Contour plots of the porosity of the material: (a) the initial porosity and (b) the porosity at the end of the analysis.
In the document, we begin by summarizing the main results in  and then describe some technical details regarding the implementation of the model in the UHYPER user subroutine. Finally, several examples of industrial interests are presented.
Reference:  Shrimali, B., Lefèvre, V., Lopez-Pamies, O. 2019. J. Mech. Phys. Solids 122, 364–380.
*Source: SIMULIA Blog