Micromechanics methods for evaluating the effective moduli of soft neo-Hookean composites

Abstract

Most biological soft tissues are multiphase composite materials, and the determination of their effective constitutive relations is a major concern in medical engineering. In this paper, we consider a class of soft two-phase composites, in which both phases are isotropic and hyperelastic neo-Hookean materials. For such an isotropic composite consisting of inclusions uniformly distributed but randomly oriented in a matrix, two constitutive parameters are required to characterize its hyperelastic constitutive relation. Micromechanics methods, including dilute concentration method, Mori–Tanaka method, self-consistent method, and differential method are extended to predict the effective properties of this kind of composites. Analytical solutions are given for the hyperelastic neo-Hookean composites reinforced by spherical particles, long fibers, and penny-shaped platelets, respectively. Finite element simulations are performed to evaluate the accuracy of these theoretical methods.