Topology optimization of structures undergoing brittle fracture

In the framework of the level-set method we propose a topology optimization algorithm for linear elastic structures which can exhibit fractures. In the spirit of Griffith theory, brittle fracture is modeled by the Francfort-Marigo energy model, with its Ambrosio-Tortorelli regularization, which can also be viewed as a gradient damage model. This quasi-static and irreversible gradient damage model is approximated using penalization to make it amenable to shape-differentiation. The shape derivative is determined using the adjoint method. The shape optimization is implemented numerically using a level-set method with body-fitted remeshing, which captures shapes exactly while allowing for topology changes. The efficiency of the proposed method is demonstrated numerically on 2D and 3D test cases. The method is shown to be efficient in conceiving crack-free structures.