On the macroscopic response, microstructure evolution, and macroscopic stability of short-fiber-reinforced elastomers at finite strains
Reza Avazmohammadi (), Pedro Ponte Castaneda (Univ. of Pennsylvania)
Prager Medal Symposium in honor of George Weng: Micromechanics, Composites and Multifunctional Materials
Mon 2:40 - 4:00
MacMillan 117
This presentation deals a constitutive model for the mechanical behavior of particle-reinforced elastomers with random microstructure subjected to finite deformations. The model is based on a recent variant of the tangent second-order (TSO) homogenization method [1] for two-phase, hyperelastic composites, and is able to directly account for the shape, orientation, and concentration of the particles. After a brief summary of the TSO homogenization method, we describe its application to composites consisting of an incompressible rubber reinforced by aligned, rigid, spheroidal particles, undergoing generally non-aligned, three-dimensional loadings. In particular, we provide analytical estimates for the overall response and microstructure evolution of the particle-reinforced composites with generalized neo-Hookean matrix phases under non-aligned loadings. For the special case of aligned pure shear and axisymmetric shear loadings, we give closed-form expressions for the effective stored-energy function of the composites with neo-Hookean matrix behavior. Moreover, we investigate the possible development of ``macroscopic'' (shear band-type) instabilities in the homogenized behavior of the composite at sufficiently large deformations. These instabilities whose wavelengths are much larger than the typical size of the microstructure are detected by making use of the loss of strong ellipticity condition for the effective stored-energy function of the composites. Finally, we provide specific applications for several representative microstructures and loading configurations, with the objective of shedding light on the intricate dependence of the macroscopic response (including the possible development of instabilities) on the nonlinear properties of the matrix, as well as on the underlying microstructure and its evolution.