Analysis of staggered evolutions for nonlinear energies in phase field fracture
Abstract
We consider a class of separately convex phase field energies employed in fracture mechanics, featuring non-interpenetration and a general softening behavior. We analyze the time-discrete evolutions generated by a staggered minimization scheme, where fracture irreversibility is modeled by a monotonicity constraint on the phase field variable. After recasting the staggered scheme by means of gradient flows, we characterize the time-continuous limits of the discrete solutions in terms of balanced viscosity evolutions, parametrized by their arc-length with respect to the L2-norm (for the phase field) and the H1-norm (for the displacement field). By a careful study of the energy balance we deduce that time-continuous evolutions may still exhibit an alternate behavior in discontinuity times.
Keywords
Cite
@article{arxiv.1904.01895,
title = {Analysis of staggered evolutions for nonlinear energies in phase field fracture},
author = {Stefano Almi and Matteo Negri},
journal= {arXiv preprint arXiv:1904.01895},
year = {2020}
}