An energy-based criterion of crack branching and its application on the multidimensional space method

In this paper, a criterion of crack branching based on the energy release rate is proposed. Theory of multidimensional space method for crack branching is established in the framework of the extended finite element method (XFEM), in which the formula of the boundary shift energy is deduced. The boundary cracking energy is obtained because the boundary shift model is abstracted into the boundary cracking model. The energy release rates of the crack branching in four quadrants are determined based on boundary cracking energy. Further, the energy release rate of the crack branching is introduced into multidimensional space method to determine the crack branching. If the crack tip branching, the criteria of crack branching are applied to determine the direction of the branching cracks, otherwise the criteria of maximum circumferential stress are applied to determine the direction of the cracks. Moreover, a classical numerical example is investigated to verify the correctness of the criterion of crack branching in the framework of the multidimensional space method. (C) 2019 Elsevier Ltd. All rights reserved.