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ABSTRACT. In the present paper we consider a numerical method for Variational Fracture based on classical finite elements with gaps, the novelty being the way in which the FE mesh is moved to approximate the cracks.
Indeed VF requires the ability to locate and approximate the crack fronts. On adopting the dicrete, “strong discontinuity” approach cracks cannot be restricted to the skeleton of a fixed FE mesh. With our method mesh is made variable: mesh nodes are taken as further unknowns and the minimization of the Energy is considered, at the same time, with respect to displacements and positions of the nodes of the mesh in the reference configuration (minimization over variable triangulations).
The results we present are still of a research type. To simplify the computations, the mesh we adopt are still too coarse to accurately catch the large values of the gradient of displacement that arise at the crack tips and so the energy. Also the descent strategy we use to solve the variational problem, though the most natural, is numerically rather slow.
The issue we try to address here is to verify the possibility of tracking cracks by using FE with gaps, without resorting to sophisticated numerical tools, by working on simple benchmark problems.