  A novel variational framework to model the fatigue behavior of brittle
materials based on a phase-field approach to fracture is presented. The
standard regularized free energy functional is modified introducing a fatigue
degradation function that effectively reduces the fracture toughness as a
proper history variable accumulates. This macroscopic approach allows to
reproduce the main known features of fatigue crack growth in brittle materials.
Numerical experiments show that the W\"ohler curve, the crack growth rate curve
and the Paris law are naturally recovered, while the approximate Palmgren-Miner
criterion and the monotonic loading condition are obtained as special cases.
