The partition of unity quadrature in element-free crack modelling

Abstract

One of the most promising application of element-free methods is the ability of analyzing crack propagation problems without the necessity of remeshing the model as the crack advances. Moreover the possibility of enriching the classical polynomial basis, introducing some integrals of the Westergaard’s solution, make the near crack tip solution accurate without requiring a very fine discretization or special treatment. In the paper the crack propagation problem is numerically analyzed by a new approach in computing the equilibrium equations. In this approach the quadrature of the variational form is not realized by introducing a background cell structure, as commonly done in literature, but by a mesh-free approach based on the partition of unity property of the shape functions. Some numerical examples illustrate the effectiveness of the method.