Gradient-enhanced damage modelling of high-cycle fatigue

Continuum damage mechanics can be used to model the initiation and growth o f fatigue cracks. However, finite element analyses using standard fatigue d amage formulations exhibit an extreme sensitivity to the spatial discretisa tion of the problem. The mesh sensitivity is caused by the fact that the un derlying continuum model predicts instantaneous, perfectly brittle crack gr owth as soon as a crack has been initiated. The growth of damage localizes in a vanishing volume during this instantaneous growth. This localization i s not so much due to loss of ellipticity of the problem, but is caused by t he 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 fin ite rate and with a positive amount of energy dissipation is predicted. Fin ite element analyses converge to this solution and are thus no longer patho logically dependent on the spatial discretization. Copyright (C) 2000 John Wiley & Sons, Ltd.