A meshless modeling of dynamic strain localization in quasi-brittle materials using radial basis function networks

Abstract

This paper describes an integrated radial basis function network (IRBFN) method for the numerical modelling of the dynamics of strain localization due to strain softening in quasi-brittle materials. The IRBFN method is a truly meshless method that is based on an unstructured point collocation procedure. We introduce a new and effective regularization method to enhance the performance of the IRBFN method and alleviate the numerical oscillations associated with weak discontinuity at the elastic wave front. The dynamic response of a one dimensional bar is investigated using both local and non-local continuum models. Numerical results, which compare favourably with those obtained by the FEM and the analytical solutions for a local continuum model, demonstrate the efficiency of the present IRBFN approach in capturing large strain gradients encountered in the present problem.