An Adaptive Cracking Particle Method for 2D Crack Propagation

Abstract

Computational modelling of fracture has been attempted in the past with a range of numerical approaches including finite element, extended finite element and meshless methods. The cracking particle method (CPM) of Rabczuk is a pragmatic alternative to explicit modelling of crack surfaces in which a crack is represented by a set of cracking particles that can be easily updated when the crack propagates. The change of cracking angle is recorded in discrete segments of broken lines, which makes this methodology suitable to model discontinuous cracks. In this paper, a new CPM is presented that improves on two counts: firstly, crack path curvature modelling is improved by the use of bilinear segments centred at each particle and secondly, efficiency for larger problems is improved via an adaptive process of both refinement and recovery. The system stiffness is calculated and stored in local matrices, so only a small influenced domain should be recalculated for each step while the remainder can be read directly from storage, which greatly reduces the computational expense. The methodology is applied to several 2D crack problems, and good agreement to analytical solutions and previous work is obtained.