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In this paper, we study fatigue failure using the variational multiscale method (VMM). In the VMM, displacement jumps are represented using finite elements with specially constructed discontinuous shape functions. These elements are progressively added along the crack path during fatigue failure. The stiffness of these elements changes non-linearly in response to the accumulation of damage during cyclic loading. The evolution law for stiffness is represented as a function of traction and the number of loading cycles since the initial onset of failure. Numerical examples illustrate the use of this new methodology for modeling macroscopic crack growth under mode I loading as well as microscopic crack growth under mixed mode loading within the elastic regime. We find that the discontinuous elements can consistently predict the mode I stress intensity factor (SIF) and the micro-structurally short crack growth paths, and that the computed Paris law for steady crack growth is controlled primarily by two parameters in the decohesion law.

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