A transition scheme from diffusive to discrete crack topologies at finite strain during the course of a staggered iterative procedure

This study presents a novel transition scheme that can trace an actual crack path as closely as possible and stably update its explicit crack tip even in a large deformation regime. The crack initiation and propagation processes are determined from an energy minimization problem with respect to the...

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Veröffentlicht in:International journal for numerical methods in engineering 2023-03, Vol.124 (6), p.1405-1433
Hauptverfasser: Han, Jike, Shintaku, Yuichi, Moriguchi, Shuji, Terada, Kenjiro
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container_issue 6
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container_title International journal for numerical methods in engineering
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creator Han, Jike
Shintaku, Yuichi
Moriguchi, Shuji
Terada, Kenjiro
description This study presents a novel transition scheme that can trace an actual crack path as closely as possible and stably update its explicit crack tip even in a large deformation regime. The crack initiation and propagation processes are determined from an energy minimization problem with respect to the displacement field and crack phase‐field, and the predicted path represented by a diffuse crack topology is replaced by a discrete path by applying the finite cover method. By developing a technique for determining explicit crack tips, the crack topology is updated from diffusive to discrete intermittently during the course of the staggered iterative procedure. Therefore, even a curved crack path that evolves significantly within a single time increment can be explicitly captured. Additionally, to stably update an explicit crack tip within the finite strain framework, we introduce a stabilization technique. Specifically, pseudo‐stiffness is applied to severely damaged elements around the discrete crack path to prevent excessively large deformations, and the corrector of the displacement increment in the global Newton–Raphson iterative procedure is intentionally diminished so that the discrete crack opens in a gradual and stable manner. After describing the individual techniques devised in the proposed scheme for achieving these features based on their algorithmic aspects, we present several representative numerical examples to demonstrate the performance and capability of the developed approach.
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Specifically, pseudo‐stiffness is applied to severely damaged elements around the discrete crack path to prevent excessively large deformations, and the corrector of the displacement increment in the global Newton–Raphson iterative procedure is intentionally diminished so that the discrete crack opens in a gradual and stable manner. 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subjects Crack initiation
crack phase‐field
Crack propagation
Crack tips
Deformation
finite cover method
finite strain
Iterative methods
staggered iterative procedure
Stiffness
strong discontinuity
Topology
title A transition scheme from diffusive to discrete crack topologies at finite strain during the course of a staggered iterative procedure
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