An analytical stress–stretch relation for porous elastomeric materials with large deformation

Porous elastomeric materials have wide applications in aerospace, electronics, biomedicine, and other fields. However, closed-form analytical solutions for macroscopic strain energy density of high-order porous elastomers have not been well resolved. In this work, we propose a new approach for constitutive modeling of porous elastomeric materials under large deformation, mainly relying on expressing the macroscopic strain energy density function of the composite material as a function of the strain energy of elastomer matrix via a strain-amplification relation. Such amplification relation, as constructed through a thick-walled sphere volume element model, is utilized in a mapping of the macroscopic deformation to the average deformation of elastomer matrix in the sense of the first invariant by a scaling coefficient–amplification factor, which depends on both the initial void volume fraction and the macroscopic volumetric deformation ratio. The analytical stress–stretch relation is then derived and given in simple form of only three material parameters. Discussions on how the factors affect the amplification factor are made and the behavior of the model is shown in several deformation simulations. The prediction results of this model are compared with those of existing models, and reasonable agreement is obtained.