GRADIENT OF DAMAGE ENHANCEMENT FOR A COHESIVE MODEL

International audienceGradient enhancements have become increasingly popular in the last decades for dealing with problems in mechanics suffering from spurious mesh sensitivity induced by strain softening. Many proposals exist in this sense and various regularization techniques have been presented and successfully applied to study localization and fracture. In short, the idea underlying almost all such techniques is that of using some extended con-stitutive equations in which information about the material microstructure is represented through a length scale-related parameter. The physical interpretation of this quantity on a micromechanical basis is still the object of an open debate, whereby its interpretation as a mere numerical regularization parameter is certainly more appropriate. From a computational standpoint, once spatial gradients and/or length scales are introduced in the constitutive equations the latter are no longer defined at the local (quadra-ture point) level but they are established at a larger scale, i.e. the scale of the structural model, in a form that could be rephrased in an integral format. Basically, for usual local models stresses, strains and internal variables are defined in a point-wise fashion whereby, as outlined in [1], their values can be regarded as the parameters of a piece-wise constant interpolation. Hence, variables computed at the Gauss point level in classical displacement-based finite element methods can be understood as fields that are in general discontinuous across elements boundaries and inside elements as well. This discontinuous pattern is indeed one of the most striking consequences of the strictly local character of the constitutive law