Implementation into OpenSees of XFEM for Analysis of Crack Propagation in Brittle Materials

Abstract

Fracture propagation simulations by means of the traditional Finite Element Method require progressive remeshing to match the geometry of the discontinuity, which heavily increases the computational effort. To overcome this limitation, methods like the eXtended Finite Element Method (XFEM), in which element nodes are enriched through the medium of Heaviside step function multiplied by nodal shape functions, may be used. The addition of a discontinuous field allows the full crack geometry to be modelled independently of the mesh, eliminating the need to remesh altogether. In this paper OpenSees framework has been used to evaluate crack propagation in brittle materials by means of the XFEM method. Two shell-type XFEM elements have been implemented into OpenSees: a three-node triangular element and a four-node quadrangular element. These elements are an improvement of the elements with drilling degrees of freedom lately suggested by the Authors [6]. The implementation of XFEM elements implied some major modifications directly into OpenSees code to take into account the rise of number of degrees of freedom in the enriched element nodes during the analysis. The developed XFEM elements have been used to evaluate crack propagation into a plane shell subject to monotonically increasing loads. Moreover, with due tuning, the modified XFEM OpenSees code can be used to study also other problems such as material discontinuities, complex geometries and contact problems.