High-Fidelity Micromechanical Modeling of Continuously Reinforced Elastic Multiphase Materials Undergoing Finite Deformations

Abstract

The purpose of this communication is twofold. First, we demonstrate the predictive capability of a recently extended micromechanics model known as the high-fidelity generalized method of cells, originally developed for unidirectionally reinforced periodic multiphase materials characterized by elastic or elasto-plastic phases undergoing infinitesimal deformation. The recent extension incorporates finite-deformation capabilities to enable modeling of heterogeneous materials such as fiber-reinforced rubbers or certain types of biological tissues characterized by potential-based, nonlinear elastic phases. The model's capability to accurately estimate both the homogenized nonlinear elastic response and the local stress fields in the individual phases is demonstrated by comparison with an exact elasticity solution for a porous composite with four different types of the matrix material under axisyrmnetric loading, and a finite-element analysis of a repeating unit cell representative of a unidirectionally reinforced periodic composite subjected to transverse loading. Second, we demonstrate the micromechanics model's utility as a subroutine in a structural analysis setting by implementing it into a specialized lamination theory framework in the absence of bending. Examples of the nonlinear response of families of [±θ]s lay-ups under biaxial inplane loading are provided, demonstrating how the developed model can be used either to validate or to construct macroscopic constitutive laws for materials, such as certain biological tissues, characterized by multi-directional reinforcement.