AbstractThe paper deals with the numerical computation of a crack problem
posed on microstructural heterogeneous materials containing multiple phases in the
microstructure. The failure of such materials is a natural multi-scale effect since cracks
typically nucleate in regions of defects on the microscopic scale. The modeling strategy
for solving the crack problem concerns simultaneously the macroscopic and microscopic
models. Our approach is based on an efficient combination of the homogenization technique
and the mesh superposition method (s-version of the finite element method). The
homogenized model relies on a double-scale asymptotic expansion of the displacement
field. The mesh superposition method uses two independent (global and local) finite
element meshes and the concept of superposing the local mesh arbitrarily on the global
continuous mesh. The crack is treated by the local mesh and the homogenized material
model is considered on the global mesh. Numerical experiments for problems on
biomorphic microcellular ceramic templates with porous microstructures of different
materials constituents are presented.