A micro-mechanical damage model based on gradient plasticity: algorithms and applications

As soon as material failure dominates a deformation process, the material increasingly displays strain softening and the nite element computation is signi cantly a ected by the element size. Without remedying this e ect in the constitutive model one cannot hope for a reliable prediction of the ductile material failure process. In the present paper, a micro-mechanical damage model coupled to gradientdependent plasticity theory is presented and its nite element algorithm is discussed. By incorporating the Laplacian of plastic strain into the damage constitutive relationship, the known mesh-dependence is overcome and computational results are uniquely correlated with the given material parameters. The implicit C1 shape function is used and can be transformed to arbitrary quadrilateral elements. The introduced intrinsic material length parameter is able to predict size e ects in material failure