Some observations on localisation in non-local and gradient damage models

Classical continuum descriptions of material degradation may cease tobe mathematically meaningful in case of softening-induced localisationof deformation. Several enhancements of conventional models have beenproposed to remove this deficiency. The properties of two of theseso-called regularisation methods, the non-local and the gradientapproach, are examined and compared in a continuum damage context. Itis shown that the enhanced models allow for the propagation of wavesin the softening zone, in contrast to conventional damage models. Forboth types of enhancement wave propagation becomes dispersive. Thebehaviour under quasi-static loading conditions is studied numerically.Finite element simulations of a one-dimensional problem yield quitesimilar results.