Homogenized elasticity solvers for biomorphic microcellular ceramics

Processing of ceramic composites from biologically derived materials has recently attained particular interest. Biomorphic microcellular silicon carbide ceramics from wood with anisotropic porous microstructures pseudomorphous to wood have been produced in the last few years. The mathematical microstructural model related to the inelastic behavior of the new composite materials is formulated. The development and implementation of optimal strategies for the mechanical performance of the ceramic composites are based on a homogenized macrostructural model. The latter is obtained by assuming a periodical distribution of the microstructure treated as an infinitesimal square periodicity cell. The homogenized elasticity coefficients are computed numerically by using a finite element discretization of the cell. Efficient solution techniques for the stationary homogenized equation in the whole domain are proposed in the case of linear elasticity.