A meshfree cell-based smoothed radial point interpolation method for damage problems

Meshfree methods belonging to the class of Smoothed Point Interpolation Methods (S-PIM) have been shown to provide certain advantages with respect to the standard finite element method (FEM), when dealing with physically nonlinear problems. The present work extends the Cell-Based Smoothed Radial Point Interpolation Method with polynomial reproduction (CS-RPIMp), originally proposed for linear problems, to the case of damage models. The weakened-weak (W2) formulation and peculiar integration scheme which this method is based on have been extended to nonlinear damage models. Some numerical examples of nonlinear problems with different kinds of boundary conditions, performed using different strategies for support nodes selection based on the T-schemes (T4-, T6/3- and T2L-schemes), are presented, aiming to point out the accuracy, convergence and efficiency of the Cell-Based Smoothed Radial Point Interpolation Method with polynomial reproduction in comparison with the standard finite element method.