A renormalization approach to model interaction in microstructured solids: Application to porous elastomer

The overall physical behavior of microstructured (heterogeneous or periodic) materials depends strongly on the size, shape, and spatial distribution of the separate constituents. To predict the macroscopic constitutive response for these materials, we apply a coarse-graining transformation – termed renormalization – developed in statistical physics that bridges between the macroscopic quantities and those at finer scales. Based on this coarse-graining transformation, a two-scale generalized model for microstructured solids is built by utilizing the mathematical framework of generalized continuum mechanics. The model is labeled as generalized because it contains extra degrees of freedom representing microscopic deformation. The present study applies the renormalization technique to develop a two-scale continuum material model for porous elastomer and implements it into commercial finite element software. Direct numerical simulation of porous elastomer computational cells is used to calibrate the model parameters. The complex effect microstructure (voids) has on constitutive behavior is examined in detail with particular attention paid to void size and distribution effects in the context of multi-axial loading, macroscopic instability (buckling), bending, and fracture.

► We apply a coarse graining approach from statistical physics for high-order continua.
► The theory is applied to porous elastomer and captures distribution effects and instability.
► Results compare well with DNS compared to conventional homogenization.