Three-dimensional Crack Propagation Analysis Using Meshless Point Collocation Method

This paper presents a meshless point collocation method for three-dimensional crack propagation. The meshless point collocation method is based on direct discretization of strong-form governing equations to achieve a truly meshless scheme that does not require mesh structures or a numerical integration procedure. These characteristics of the point collocation method enable the direction of an arbitrary crack propagation to be defined purely according to the fracture criterion of the mechanical model because node-wise topology can be easily transformed by the simple addition of nodes and polygonal surfaces. The main advantages of the presented method are that there is no need to consider the consistency between the mesh connectivity and continuity of fracture zone locations and that the crack propagation procedure is relatively simplified with no additional implementation features from numerical integration used in weak formulations. The constrained moving least squares approximation (C-MLS) is employed for meshless interpolation so that essential boundary conditions can easily be applied. A cohesive crack model is directly introduced in combination with the crack growth procedure to express the fracture of quasi-brittle materials such as concrete. The accuracy and robustness of the presented method were demonstrated through its application to several numerical examples.