Multilevel global–local techniques for adaptive ductile phase-field fracture

authored by
Fadi Aldakheel, Nima Noii, Thomas Wick, Olivier Allix, Peter Wriggers
Abstract

This paper outlines a rigorous variational-based multilevel Global-Local formulation for ductile fracture. Here, a phase-field formulation is used to resolve failure mechanisms by regularizing the sharp crack topology on the local state. The coupling of plasticity to the crack phase-field is realized by a constitutive work density function, which is characterized through a degraded stored elastic energy and the accumulated dissipated energy due to plasticity and damage. Two different Global-Local approaches based on the idea of multiplicative Schwarz' alternating method are proposed: (i) A global constitutive model with an elastic-plastic behavior is first proposed, while it is enhanced with a single local domain, which, in turn, describes an elastic-plastic fracturing response. (ii) The main objective of the second model is to introduce an adoption of the Global-Local approach toward the multilevel local setting. To this end, an elastic-plastic global constitutive model is augmented with two distinct local domains; in which, the first local domain behaves as an elastic-plastic material and the next local domain is modeled due to the fracture state. To further reduce the computational cost, predictor-corrector adaptivity within Global-Local concept is introduced. An adaptive scheme is devised through the evolution of the effective global plastic flow (for only elastic-plastic adaptivity), and through the evolution of the local crack phase-field state (for only fracture adaptivity). Thus, two local domains are dynamically updated during the computation, resulting with two-way adaptivity procedure. The overall response of the Global-Local approach in terms of accuracy/robustness and efficiency is verified using single-scale problems. The resulting framework is algorithmically described in detail and substantiated with numerical examples.

Organisation(s)
Institute of Continuum Mechanics
Institute of Applied Mathematics
PhoenixD: Photonics, Optics, and Engineering - Innovation Across Disciplines
External Organisation(s)
Université Paris-Saclay
École normale supérieure Paris-Saclay
Centre national de la recherche scientifique (CNRS)
Type
Article
Journal
Computer Methods in Applied Mechanics and Engineering
Volume
387
ISSN
0045-7825
Publication date
15.12.2021
Publication status
Published
Peer reviewed
Yes
ASJC Scopus subject areas
Computational Mechanics, Mechanics of Materials, Mechanical Engineering, Physics and Astronomy(all), Computer Science Applications
Electronic version(s)
https://arxiv.org/abs/2103.02377v1 (Access: Open)
https://doi.org/10.1016/j.cma.2021.114175 (Access: Closed)