It is difficult to simulate fracture propagation on linear elastic
composite materials due to their heterogeneous nature. While Linear
Elastic Fracture Mechanics (LEFM) provides a solid theoretical framework
for fracture on homogeneous materials, it is unclear how to proceed
when highly heterogeneous materials are considered. One possibility is
to assume that the assumptions of LEFM are still valid within each of
the constituents of the composite. In this case, the fracture problem
may be formulated as a problem of linear elasticity with heterogeneous
coefficients, to which a fracture condition must be added. Solving this
elasticity problem is quite difficult, as classical methods such as the
finite element method would require a prohibitively fine mesh. In this
talk, we will discuss some alternative solutions. |