Manifold Method and Its Applications for Modeling Fracturing in Solids

A numerical technique based on using manifold elements in finite element method, for modeling propagation of arbitrary cracks in solids, is described. When the region with crack(s)is subjected to external loading and the crack(s) starts to extend, the crack growth may intersect boundaries of nearby finite elements. Those intersected finite elements are replaced by manifold elements. The technique, by which the initial finite element mesh can be kept unchanged during the processes of crack propagation, is called manifold elements in finite element method. The crack growth is governed by the theories of linear elastic fracture mechanics. The stress intensity factors are computed by a contour integral technique and crack trajectory is determined by applying the maximum tangential stress criterion. Finally, test examples are given to verify the new method and the predicted trajectories are compared to experimentally obtained crack growth paths with good agreements