Adaptive Exponential Finite Elements for a Phase Field Fracture Model
- Fracture phenomena can be described by a phase field model in which an independent scalar field variable in addition to the mechanical displacement is considered [3]. This field approximates crack surfaces as a continuous transition zone from a value that indicates intact material to another value that represents the crack. For an accurate approximation of cracks, narrow transition zones resulting in steep gradients of the fracture field are required. This necessitates a high mesh density in finite element simulations, which leads to an increased computational effort. In order to circumvent this problem without forfeiting accuracy, exponential shape functions were introduced in the discretization of the phase field variable, see [4]. These special shape functions allow for a better approximation of steep gradients of the phase field with less elements as compared to standard Lagrange elements. Unfortunately, the orientation of the exponential shape functions is not uniquely determined and needs to be set up in the correct way in order to improve the approximation of smooth cracks. This work solves the issue by adaptively reorientating the exponential shape functions according to the nodal values of the phase field gradient in each element. Furthermore, a local approach is pursued that uses exponential shape function only in the vicinity of the crack, whereas standard bilinear shape function are used away from the crack.
Author: | Darius Olesch, Charlotte Kuhn, Alexander Schlüter, Ralf Müller |
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URN: | urn:nbn:de:hbz:386-kluedo-80117 |
DOI: | https://doi.org/10.1002/pamm.202100077 |
ISSN: | 1617-7061 |
Parent Title (English): | Proceedings in Applied Mathematics and Mechanics |
Publisher: | Wiley |
Document Type: | Article |
Language of publication: | English |
Date of Publication (online): | 2024/04/12 |
Year of first Publication: | 2021 |
Publishing Institution: | Rheinland-Pfälzische Technische Universität Kaiserslautern-Landau |
Date of the Publication (Server): | 2024/04/12 |
Issue: | 21/1 |
Page Number: | 2 |
Source: | https://onlinelibrary.wiley.com/doi/10.1002/pamm.202100077 |
Faculties / Organisational entities: | Kaiserslautern - Fachbereich Maschinenbau und Verfahrenstechnik |
DDC-Cassification: | 6 Technik, Medizin, angewandte Wissenschaften / 620 Ingenieurwissenschaften und Maschinenbau |
Collections: | Open-Access-Publikationsfonds |
Licence (German): | Zweitveröffentlichung |