Finite Strain Micromechanical Modeling of Multiphase Composites

This paper reviews a series of articles in which finite strain micromechanical analyses were developed for the prediction of the macroscopic (global) behavior of multiphase composites undergoing large deformations. The finite strain constituents in these composites can be modeled as hyperelastic, thermoelastic (based on entropic elasticity), viscoelastic (including quasilinear viscoelasticity, which is suitable for the modeling of bilogical tissues), thermoviscoelastic, rate-dependent thermoinelastic (viscoplastic), and rate-independent thermoinelastic (elastoplastic). In all cases, the micromechanical analyses are based on the homogenization technique for periodic composites. These analyses provide the instantaneous mechanical, thermal, and inelastic concentration tensors that relate the local induced strain in the phase to the current externally applied strains and temperature. In addition, these micromechanical analyses yield the macroscopic constitutive equations of the multiphase composite in terms of its instantaneous stiffness and thermal stress tensors. In any one of these micromechanical analyses, the local field distribution among the various constituents of the composite can be also determined at any instant of loading. The finite strain micromechanically established macroscopic constitutive equations can be employed in a structural analysis to determine the behavior of composite structures and biological tissues underging large deformations, thus forming a micro macrostructural multiscale analysis.