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

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 approach is to introduce an adoption of the Global-Local model toward the multilevel local setting. In (ii), 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 second local domain is modeled due to the fractured state. To further reduce the computational cost, predictor-corrector adaptivity within the 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 in a 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. (c) 2021 Elsevier B.V. All rights reserved.

Automated summary

This paper presents a rigorous variational-based multilevel Global-Local formulation for ductile fracture, using phase-field method and constitutive work density function to address plasticity and damage. Two Global-Local approaches are proposed, one with a global constitutive model coupled with a single local domain, and the other with a global constitutive model coupled with two local domains. The introduction of predictor-corrector adaptivity within the Global-Local concept aims to reduce computational costs and improve accuracy and efficiency.