Microscopic and Macroscopic Instabilities in Particle-Reinforced Elastomers
Résumé
In this work, we carry out a thorough investigation of microscopic instabilities—including short-wave-length bifurcations, cavitation, decohesion, and fiber contact—and macroscopic instabilities—defined as the loss of strict rank-one convexity of the effective properties—in particle-reinforced elastomers subjected to finite deformations. Specifically, we consider isotropic hyperelastic solids reinforced with: i) random and ii) periodic distributions of elliptical rigid particles. The results are computed by means of the analytical second-order homogenization approximation method (SOH), as well as with more accurate finite element method (FEM) calculations. It is found that the manner in which the material fails depends greatly on the evolution of the underlying microstructure, which in turn depends directly on the type of applied loading conditions: i) for compressive modes of deformation, the material is found to become unstable via short-wave-length bifurcations and fiber contact, ii) for tensile modes of deformation, the material undergoes cavitation and decohesion. Moreover, it is found that materials with random distribution of particles are significantly more stable than those with periodic distributions.