Overall Mechanical Response of Particle-Reinforced Elastomers at Finite Strains

[img_assist|nid=15079|title=Elastomers Reinforced by Spherical Particles Under Different Loading Conditions|desc=|link=none|align=left|width=300|height=264]Abstract An approximate homogenization method is proposed and used to obtain estimates for the effective constitutive behavior and associated microstructure evolution in hyperelastic composites undergoing finite-strain deformations. The method yields a constitutive relation accounting for the evolution of characteristic features of the underlying microstructure in the composites, when subjected to large deformations. The method is applied to elastomers containing random distributions of aligned, rigid, ellipsoidal inclusions, and explicit analytical estimates are obtained for the special case of spherical inclusions distributed isotropically in an incompressible neo-Hookean matrix. In addition, the method is also applied to two-dimensional composites with random distributions of aligned, elliptical fibers, and the results are compared with corresponding results of earlier homogenization estimates and finite element simulations.