Fracture resistance via topology optimization

The fracture resistance of structures is optimized using the level-set method. Fracture resistance is assumed to be related to the elastic energy released by a crack propagating in a normal direction from parts of the boundary that are in tension, and is calculated using the virtual crack extension technique. The shape derivative of the fracture-resistance objective function is derived. Two illustrative two-dimensional case studies are presented: a hole in a plate subjected to biaxial strain; and a bridge fixed at both ends subjected to a single load in which the compliance and fracture resistance are jointly optimized. The structures obtained have rounded corners and more material at places where they are in tension. Based on the results, we propose that fracture resistance may be modeled more easily but less directly by including a term proportional to surface area in the objective function, in conjunction with nonlinear elasticity where the Young's modulus in tension is lower than in compression.