Numerical simulations of strain localization in inelastic solids using mesh-free methods

In this paper, a comprehensive account on using mesh-free methods to simulate strain localization in inelastic solids is presented. Using an explicit displacement-based formulation in mesh-free computations, high-resolution shear-band formations are obtained in both two-dimensional (2-D) and three-dimensional (3-D) simulations without recourse to any mixed formulation, discontinuous/incompatible element or special mesh design. The numerical solutions obtained here are insensitive to the orientation of the particle distributions if the local particle distribution is quasi-uniform, which, to a large extent, relieves the mesh alignment sensitivity that finite element methods suffer. Moreover, a simple h-adaptivity procedure is implemented in the explicit calculation, and by utilizing a mesh-free hierarchical partition of unity a spectral (wavelet) adaptivity procedure is developed to seek high-resolution shear-band formations. Moreover, the phenomenon of multiple shear band and mode switching are observed in numerical computations with a relatively coarse particle distribution in contrast to the costly fine-scale finite element simulations.