A Theory of Multi-Constituent Finitely-Deforming Composite Materials Subject to Thermochemical Changes with Damage

Abstract

A mixture theory with arbitrary numbers of constituents of anisotropic solids and fluids, invoking the postulate of maximum rate of entropy production with coupled diffusion, reaction, deformation and thermal history, is briefly described. The model generalizes the 2-constituent theory of Hall and Rajagopal (2012) to include, in addition to the previously-described features, multiplicatively decomposed kinematics for thermal and chemical volume expansions and contractions. Applications of interest generally include the evolution of asymmetric material features involving finite-dimensional growth and recession, leading to local rotations important to the description of failure. An example process is the oxidation of SiC to form SiO₂ in SiC-based ceramic matrix composites (CMCs), which results in a 2.2× local volume increase.

A damage approach is described that relies on the decomposition of the internal energy into non-dissipative and dissipative parts applied within the principle of virtual power.