# Loaded crack surfaces in two and three dimensions with XFEM

Markus Schätzer, Thomas Peter Fries

Publikation: Beitrag in einer FachzeitschriftArtikelForschungBegutachtung

### Abstract

A numerical framework in two and three dimensions is proposed for crack propagation induced by loaded crack surfaces. The method is based on the XFEM with a hybrid explicit-implicit crack description. The load on the crack surface is given on the explicit surface mesh and transferred to the zero-level set of the implicit description. Therefore, integration points must be identified on the zero-level set which are also used to determine stress intensity factors by crack opening displacements. A crack propagation model is developed where the load factor of the crack surface loading is determined such that the criterion for crack propagation is met. Numerical results show the versatility and success of the approach.

Originalsprache englisch 863-885 23 Applied Mathematical Modelling 78 https://doi.org/10.1016/j.apm.2019.10.020 Veröffentlicht - 1 Feb 2020

### Fingerprint

Surface Crack
Crack Propagation
Three-dimension
Two Dimensions
Zero set
Cracks
Level Set
Crack
Crack propagation
Stress Intensity Factor
Mesh
Numerical Results
Stress intensity factors
Model

### ASJC Scopus subject areas

• !!Modelling and Simulation
• Angewandte Mathematik

### Fields of Expertise

• Information, Communication & Computing

### Dies zitieren

in: Applied Mathematical Modelling, Jahrgang 78, 01.02.2020, S. 863-885.

Publikation: Beitrag in einer FachzeitschriftArtikelForschungBegutachtung

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AB - A numerical framework in two and three dimensions is proposed for crack propagation induced by loaded crack surfaces. The method is based on the XFEM with a hybrid explicit-implicit crack description. The load on the crack surface is given on the explicit surface mesh and transferred to the zero-level set of the implicit description. Therefore, integration points must be identified on the zero-level set which are also used to determine stress intensity factors by crack opening displacements. A crack propagation model is developed where the load factor of the crack surface loading is determined such that the criterion for crack propagation is met. Numerical results show the versatility and success of the approach.

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KW - Critical pressure

KW - Data transfer

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