A phenomenological approach to fatigue with a variational phase-field model: The one-dimensional case

We propose a new variational fatigue phase-field model. The basic idea of the model is to let the fracture energy decrease as a suitably defined accumulated strain measure increases, which is obtained by introducing a dissipation potential which explicitly depends on the strain history. This amounts to a phenomenological description of a multitude of microscopic material degradation mechanisms, that are responsible for the macroscopic evidence of fatigue effects. In this first step of a longer term project, the analysis is limited to the simplest possible setting, namely: linear elasticity, brittle material behavior, symmetric response in tension and compression. However, in this variational framework, the extension to include additional material phenomena, such as plasticity, is straightforward. We show the results of numerical simulations based on a solution strategy devised from the variational approach. Already with the choice of simple constitutive functions, based on few key constitutive parameters, the present model is capable to describe typical σ-N (Wöhler) curves, to recover the known trends in the description of the mean-stress effects and to account for generic loads in a straightforward manner.