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The main aim of this work is investigation of localization problem in strain softening materials and regularization techniques, which will reduce and possibly remove mesh dependency of the numerical results and balance the effects of heterogeneous microstructure on local continua while keeping the boundary value problem of softening (damaged) continua well-posed. Finite Element Method (FEM) and Smooth Particle Hydrodynamic (SPH) combined with a local continuum damage model (CDM) were used for analysis of a dynamic stress wave propagation problem, which was analytically solved in (Bažant and Belytschko 1985). The analytical solution was compared to the numerical results, obtained by using a stable, Total-Lagrange form of SPH (Vignjevic et al. 2006, Vignjevic et al. 2009), and two material models implemented in the FEM based on: 1) classic CDM; and 2) equivalent damage force. The numerical results demonstrate that the size of the damaged zone is controlled by element size in classic FEM and the smoothing length in the SPH, which suggests that the SPH method is inherently non-local method and that the smoothing length should be linked to the material characteristic length scale in solid mechanics simulations.

LOCALIZATION AND DAMAGE INDUCED SOFTENING USING FINITE ELEMENT AND SMOOTH PARTICLE HYDRODYNAMIC METHODS