  The fracture resistance of structures is optimised 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 which 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 optimised. 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 modelled more easily but less directly
by including a term proportional to surface area in the objective function, in
conjunction with non-linear elasticity where the Young's modulus in tension is
lower than in compression.
