Discretization influence in strain—softening problems

The dispersive behaviour of waves in softening problems is analysed. Attention is focused on the influence of the numerical scheme on the dispersion characteristics in the process of localization of deformation. Distinction has been made between softening models defined in a standard plasticity framework and in a gradient‐dependent plasticity theory. Waves in a standard softening plasticity continuum do not disperse but due to spatial discretization dispersion is introduced which results in a mesh size dependent length scale effect. On the other hand, wave propagation in a gradient‐dependent softening plasticity continuum is dispersive. By carrying out the dispersion analysis on the discretized system the influence of numerical dispersion on material dispersion can be quantified which enables us to determine the accuracy for the solution of the localization zone. For a modelling with and without the inclusion of strain gradients accuracy considerations with respect to mass discretization, finite element size, time integration scheme and time step have been carried out.