A meshless IRBFN-based numerical simulation of dynamic strain localization in quasi-brittle materials

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. The integration approach is the key to achieving accurate function derivatives necessary for numerical stability and solution accuracy. A new coordinate mapping technique for the IRBFN method is introduced in this paper to resolve the steep velocity, strain and strain-rate gradients associated with the strain localisation process. The behaviour of a one dimensional bar is investigated using a nonlocal damage model governed by a Telegraph-type constitutive relation. The bar is dynamically loaded in tension with a constant end velocity. The strain waves propagating from the two ends meet at the centre of the bar and causes a large strain increase at this location. This strain increase, under suitable conditions, will initiate the strain localisation process due to the strainsoftening constitutive behaviour of the material. Numerical results obtained compare favourably with those obtained by the FEM and demonstrate the efficiency of the present IRBFN approach in solving steep (singularity-like behaviour) nonlinear PDEs