Modeling two-phase hyperelastic media by infinite-rank laminates

M. I. IDIART; O. LOPEZ-PAMIES

Boston (MA)

Congreso; 2008 ASME International Mechanical Engineering Congress & Exposition; 2008

American Society of Mechanical Engineers

New theoretical predictions are presented for the macroscopic response of random porous elastomers. The predictions follow from a suitable formulation of the homogenization approach recently proposed by Idiart (J. Mech. Phys. Solids 2008) for nonlinear composites. The central idea behind this approach is to model the microstructure by sequentially laminated constructions of infinite rank, whose macroscopic stored-energy function can be determined exactly. The resulting estimates incorporate microstructural information up to the two-point correlation functions, and require the solution to a Hamilton-Jacobi equation with the pore volume fraction and the macroscopic deformation gradient playing the role of `time´ and `spatial´ variables, respectively. Because they are realizable, by construction, these estimates are guaranteed to satisfy all pertinent bounds and constraints imposed by the local constitutive behavior (e.g., incompressibility). Sample results for two-dimensional systems are provided and compared with recent `linear comparison´ homogenization estimates and exact results available from the literature.