An adaptive mesh scheme of the lattice spring model based on geometrical continuity

Abstract

An adaptive mesh scheme is introduced for the lattice spring model (LSM), where the original triangular cells are subdivided into a set of smaller triangular cells. The scheme is based on geometrical continuity at the heterogeneous mesh boundary, where the refined grid cells intersect the original cell edge. The LSM simulations on the refined grid show a superior computational efficiency to the uniform grid. Each subdivision reduces the original cell edges by a factor of two. The refinement procedure was recursively applied ten times before any marked loss in accuracy was observed. The accuracy of the adaptive model is on par with a regular grid approach. More specifically, the characteristics of fracture cavity are comparable with a uniform grid of the same mesh density as the smallest cells in the adaptive approach. The fracture criterion such as J-integral, the elastic energy of the grid and potential energy change due to fracture growth and strain loading agree well with the theory of a mode I fracture, which enables simulations of process such as sub-critical fracture with a wide dynamic range.