Wave propagation and localisation in nonlocal and gradient-enhanced damagemodels

Classical continuum descriptions of material degradation may cease to be ma thematically meaningful in case of softening-induced localisation of deform ation. Several enhancements of conventional models have been proposed to re move this deficiency. The properties of two of these so-called regularisati on methods, the nonlocal and the gradient approaches, are examined and comp ared in a continuum damage context. It is shown that the enhanced models al low for the propagation of waves in the softening zone, in contrast to conv entional damage models. For both types of enhancement wave propagation beco mes dispersive. The behaviour under quasi-static loading conditions is stud ied numerically. Finite element simulations of a one-dimensional problem yi eld quite similar results for the nonlocal and a gradient-enhanced model. T he gradient enhancement has been used to model concrete fracture, yielding results which are in good agreement with experimental data.