Gradient-enhanced damage modelling of high-cycle fatigue

Continuum damage mechanics can be used to model the initiation and growth of fatigue cracks. However, nite element analyses using standard fatigue damage formulations exhibit an extreme sensitivity to the spatial discretisation of the problem. The mesh sensitivity is caused by the fact that the underlying continuum model predicts instantaneous, perfectly brittle crack growth as soon as a crack has been initiated. The growth of damage localizes in a vanishing volume during this instantaneous growth. This localization is not so much due to loss of ellipticity of the problem, but is caused by the fact that the damage rate is singular at the crack tip. The damage rate singularity can be removed by the introduction of higher-order deformation gradients in the constitutive modelling. As a result, crack growth at a nite rate and with a positive amount of energy dissipation is predicted. Finite element analyses converge to this solution and are thus no longer pathologically dependent on the spatial discretization