Peridynamics with Corrected Boundary Conditions and Its Implementation in Multiscale Modeling of Rolling Contact Fatigue

There is a boundary effect due to incomplete horizons of boundary or near-boundary points in peridynamics. In this paper, we propose to attach “fictitious walls” to boundary surfaces so that the boundary effect can be reduced or eliminated. Differing from the concept of “fictitious material layers”, which is only attached to displacement boundary surfaces, “fictitious walls” are attached to both displacement and force boundary surfaces. Three types of fictitious walls are considered in this paper: undeformed, deformed, and periodic. It is recommended to attach “undeformed fictitious walls” to displacement boundaries and “deformed fictitious walls” to force boundaries. “Periodic fictitious walls” are suggested for use in peristatics only. In addition, peridynamics with corrected boundary conditions is then implemented in a hierarchical multiscale method to study rolling contact fatigue. In this hierarchical multiscale framework, the coefficient of friction is passed from molecular dynamics simulations to peridynamics, which models crack initiation and propagation in rolling contact simulations.