Enhanced damage modelling of quasi-brittle and fatigue fracture : computational aspects

Continuum damage mechanics can be used to model the initiation and growth of cracks. However, ??nite element analyses using standard fatigue damage formulations exhibit an extreme sensitivity to the spatial discretisation of the problem. Nonlocal and gradient damage formulations do not exhibit this mesh sensitivity. But the nonlocality or gradient terms in these models require some modi??fications of standard ??nite element algorithms for damage mechanics. In particular, care must be taken that the continuum representation of a crack is separated from the remaining material by applying the correct boundary conditions and remeshing the problem domain. For high-cycle fatigue analyses, special time integration schemes are needed to limit the computational e??ort involved. With these enhancements, reliable and mesh objective ??nite element analyses of crack initiation and growth become feasible, as is demonstrated by an application in metal fatigue.