DISCRETIZATION INFLUENCE IN STRAIN-SOFTENING PROBLEMS

The dispersive behaviour of waves in softening problems is analysed. A ttention is focused on the influence of the numerical scheme on the di spersion characteristics in the process of localization of deformation . Distinction has been made between softening models defined in a stan dard plasticity framework and in a gradient-dependent plasticity theor y. Waves in a standard softening plasticity continuum do not disperse but due to spatial discretization dispersion is introduced which resul ts in a mesh size dependent length scale effect. On the other hand, wa ve propagation in a gradient-dependent softening plasticity continuum is dispersive. By carrying out the dispersion analysis on the discreti zed system the influence of numerical dispersion on material dispersio n can be quantified which enables us to determine the accuracy for the solution of the localization zone. For a modelling with and without t he inclusion of strain gradients accuracy considerations with respect to mass discretization, finite element size, time integration scheme a nd time step have been carried out.