On safe crack shapes in elastic bodies

According to the Griffith criterion, a crack propagation occurs, provided that the derivative of the energy functional with respect to the crack length reaches some critical value. We consider a generalization of this criterion to the case of nonlinear cracks satisfying a nonpenetration condition and investigate the dependence of the shape derivative of the energy functional on the crack shape. In the paper, we find the crack shape which gives the maximal deviation of the energy functional derivative from a given critical value and, in particular, prove that this optimality problem admits a solution.