Discrete crack modelling in a new X-FEM format with emphasis on dynamic response

Journal article, 2007

The displacement field in quasi-brittle material is localized into narrow fracture zones during the process of decohesion. The numerical modelling of the physically propagating displacement discontinuities is considered to be inherently difficult. In this paper, the introduction of continuous discontinuities into the finite element formulation is based on the extended finite element method (X-FEM). This paper extends the theory by further incorporating arbitrary discontinuities in the approximation and presenting numerical procedures to handle several fields of discontinuities. The discontinuous approximation is accomplished by usage of basis functions of very limited support; only non-zero in the elements containing the crack. Moreover, the introduction of discontinuities in a continuum is discussed and a robust numerical procedure is proposed. Further, the mechanical behaviour of cracks in a quasi-brittle material largely governs the overall mechanical response of the material, and the implementation of a cohesive crack model based on anisotropic damage coupled to plasticity is emphasized. Numerical examples for both static and dynamic, transient, loading show that the proposed X-FEM format in combination with the cohesive crack model has a good performance and leads to an efficient implementation. Finally, the proposed forward method for propagation of cracks and introduction of new ones is robust and stable. Copyright (c) 2006 John Wiley & Sons, Ltd.