Comparison of the performance of SSPH and MLS basis functions for two-dimensional linear elastostatics problems including quasistatic crack propagation

We use symmetric smoothed particle hydrodynamics (SSPH) and moving least squares (MLS) basis functions to analyze six linear elastostatics problems by first deriving their Petrov-Galerkin approximations. With SSPH basis functions one can approximate the trial solution and its derivatives by using different basis functions whereas with MLS basis functions the derivatives of the trial solution involve derivatives of the basis functions used to approximate the trial solution. The class of allowable kernel functions for SSPH basis functions includes constant functions which are excluded in MLS basis functions if derivatives of the trial solution are also to be approximated. We compare results for different choices of weight functions, size of the compact support of the weight function, order of complete polynomials, and number of particles in the problem domain. The two basis functions are also used to analyze crack initiation and propagation in plane stress mode-I deformations of a plate made of a linear elastic isotropic and homogeneous material with particular emphasis on the computation of the T-stress. The crack trajectories predicted by using the two basis functions agree well with those found experimentally.