Mechanics and geometry of nonlinear cracks: A complex stress-function approach

A central method for solving linear elastic problems in domains of low symmetry is by complexifying the elastic potential and using conformal maps to transform the domain of interest to a simpler one, e.g. from a crack to a circular hole. The elastic fields calculated at the vicinity of a crack in this approach are not small, and therefore question the validity of linear elasticity. Here we present a new method that allows us to generalise the complex function approach to nonlinear elasticity. We implement our method to solve the nonlinear problem of a crack, and upon comparing with earlier attempt to this problem we address open questions about the (un)ambiguity of this mechanical problem.