Multilevel Global-Local techniques for adaptive ductile phase-field fracture

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.

arXiv comment50 pages, 24 Figures, 4 Tables

References in corpus (5)

• Non-overlapping domain decomposition methods in structural mechanics
• An Adaptive Global-Local Approach for Phase-Field Modeling of Anisotropic Brittle Fracture
• A Phase-Field Description for Pressurized and Non-Isothermal Propagating Fractures
• Bayesian Inversion for Anisotropic Hydraulic Phase-Field Fracture
• On the computation of plate assemblies using realistic 3D joint model: a non-intrusive approach

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• Efficient flexible boundary conditions for long dislocations
• Probabilistic failure mechanisms via Monte Carlo simulations of complex microstructures