Some Remarks on the Numerical Modelling of Localized Failure

Abstract

An efficient numerical framework suitable for three-dimensional analyses of brittle material failure is presented. The proposed model is based on an (embedded) Strong Discontinuity Approach (SDA). Hence, the deformation mapping is elementwise additively decomposed into a conforming, continuous part and an enhanced part associated with the kinematics induced by material failure. To overcome locking effects and to provide a continuous crack path approximation, the approach is extended and combined with advantages known from classical interface elements. More precisely, several discontinuities each of them being parallel to a facet of the respective finite element are considered. By doing so, crack path continuity is automatically fulfilled and no tracking algorithm is necessary. However, though this idea is similar to that of interface elements, the novel SDA is strictly local (finite element level) and thus, it does not require any modification of the global data structure, e.g., no duplication of nodes. An additional positive feature of the advocated finite element formulation is that it leads to a symmetric tangent matrix. It is shown that several simultaneously active discontinuities in each finite element are required to capture highly localized material failure. The performance and predictive ability of the model are demonstrated by means of two benchmark examples.