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Some observations on localisation in non-local and gradient damage models. (English) Zbl 0891.73055
Summary: Classical continuum descriptions of material degradation may cease to be mathematically meaningful in case of softening-induced localization of deformation. Several enhancements of conventional models have been proposed to remove this deficiency. The properties of two of these so-called regularization methods, the non-local and the gradient approach, are examined and compared in a continuum damage context. It is shown that the enhanced models allow for the propagation of waves in the softening zone, in contrast to conventional damage models. For both types of enhancement, wave propagation becomes dispersive. The behaviour under quasi-static loading conditions is studied numerically. Finite element simulations of a one-dimensional problem yield quite similar results.

74R99 Fracture and damage