12. Solution Approach for Coupled Diffusion-Reaction-Deformation Problems in Anisotropic Materials

A capability to model oxidizing carbon-fiber polyimide matrix composites has evolved over the past number of years at Air Force Research Laboratory [1]. Quoting [1] regarding a unidirectional non-woven fibrous layer, without cracks, “The [finite element model] requires mesh sizes in the 1-μm scale and time increments in 1-s steps. A 200-h oxidation simulation with 100-μm oxidation zone size typically requires problem sizes in the order of 100,000 degrees of freedom (DOF) and 720,000 time steps.” Because of interest in a number of related problem classes including structural component scales, desire to incorporate process restrictions offered by thermodynamics, and the possible involvement of finite deformations, a mixture theory approach was developed by Hall and Rajagopal [2]. The theory is based on two constituents, an anisotropic viscous fluid and an anisotropic hyperelastic solid, which react with each other. The model considers the comparatively simple cases where conversions of species, including the associated masses, linear and angular momenta, energies and entropies, are limited to interchanges between the original fluid and solid.