Consistent Finite-Dimensional Approximation of Phase-Field Models of Fracture
Numerical Analysis
2019-03-07 v1
Abstract
In this paper we focus on the finite-dimensional approximation of quasi-static evolutions of critical points of the phase-field model of brittle fracture. In a space discretized setting, we first discuss an alternating minimization scheme which, together with the usual time-discretization procedure, allows us to construct such finite-dimensional evolutions. Then, passing to the limit as the space discretization becomes finer and finer, we prove that any limit of a sequence of finite-dimensional evolutions is itself a quasi-static evolution of the phase-field model of fracture. In particular, our proof shows for the first time the consistency of numerical schemes related to the study of fracture mechanics and image processing.
Keywords
Cite
@article{arxiv.1707.00578,
title = {Consistent Finite-Dimensional Approximation of Phase-Field Models of Fracture},
author = {Stefano Almi and Sandro Belz},
journal= {arXiv preprint arXiv:1707.00578},
year = {2019}
}