Abstract

In this talk I will present applications of the “variational linear comparison” nonlinear homogenization technique to generate estimates for the effective behavior, microstructure evolution and loss of ellipticity in reinforced elastomers at finite strains. Three special cases will be considered for illustrative purposes: short-fiber composite elastomers, long-fiber reinforced rubbers and thermoplastic elastomers (TPEs). In particular, for the short-fiber composites, we investigate the rotation of the rigid particles in the context of finite elasticity, and make comparisons with Jeffery’s solution for rigid particles in a Newtonian fluid. For the long-fiber composites, we make comparisons with Rosen’s estimates for the possible development of instabilities (using a two-dimensional laminate model). For the TPEs, which are block copolymer systems with a hard glassy phase serving to provide reinforcement in a softer rubbery matrix phase, we explore the effect of structure at two different length scales: a lamellar structure at the nanometer scale and a granular structure at the micrometer scale. In all these material systems, it is found that even when the constituent phases are strongly elliptic, their overall behavior may lose ellipticity at sufficiently large deformations, corresponding to the possible development of shear band-type instabilities. The source of these “macroscopic” instabilities has been identified with the evolution of the microstructure, which, under appropriate loading conditions, can induce “geometric softening” leading to the overall loss of ellipticity.