Gradient-enhanced damage modelling of high-cycle fatigue

Continuum damage mechanics can be used to model the initiation and growthof fatigue cracks. However, finite element analyses using standard fatiguedamage formulations exhibit an extreme sensitivity to the spatialdiscretisation of the problem. The mesh sensitivity is caused by the factthat the underlying continuum model predicts instantaneous, perfectlybrittle crack growth as soon as a crack has been initiated. The growth ofdamage localises in a vanishing volume during this instantaneous growth.This localisation is not so much due to loss of ellipticity of theproblem, but is caused by the fact that the damage rate is singular at thecrack tip. The damage rate singularity can be removed by the introductionof higher-order deformation gradients in the constitutive modelling. As aresult, crack growth at a finite rate and with ! a positive amount of energydissipation is predicted. Finite element analyses converge to thissolution and are thus no longer pathologically dependent on the spatialdiscretisation.