Gradient damage models: Toward full-scale computations

The description of localisation and structural failure through local damage constitutive laws leads to ill-posed problems. To retrieve a well-posed problem, the material state is described through the gradients of damage in addition to the strain and the damage. Under some assumptions, it is shown that these gradient laws can be cast into a variational formulation. Its numerical treatment is reduced to the design of a mixed finite element so that algorithms such as Newton’s method and path-following techniques are still available. Possible convergence difficulties related to the reduction of the damage band width and the appearance of micro instabilities are removed thanks to the design of a new class of brittle laws. Finally, numerical applications show the convergence with mesh refinement, the compatibility with coarser approaches such as Griffith’s theory and cohesive crack models, the robustness in case of unstable multi-cracking, the applicability to full-scale 3D situations and the physical relevance compared to experimental data.