A J-integral-based arc-length solver for brittle and ductile crack propagation in finite deformation-finite strain hyperelastic solids with an application to graphene kirigami

The method proves able to handle very sudden snap-backs occurring under large strains, and both brittle and ductile crack propagation. A particular example of such behaviour is kirigami (paper-cuts) structures made of graphene. The proposed arc-length can capture, for these structures, the transitions from brittle to ductile crack propagation for the same crack patterns, but different pre-crack lengths.