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. |