Consistent Finite-Dimensional Approximation of Phase-Field Models of Fracture

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.

Cited by in corpus (3)

• Analysis of staggered evolutions for nonlinear energies in phase field fracture
• Irreversibility and alternate minimization in phase field fracture: a viscosity approach
• Approximation of the Mumford-Shah Functional by Phase Fields of Bounded Variation