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# A Phase Field Modeling Approach of Crack Growth in Materials with Anisotropic Fracture Toughness

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OASIcs.iPMVM.2020.9.pdf
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## Cite As

Christoph Schreiber, Tim Ettrich, Charlotte Kuhn, and Ralf Müller. A Phase Field Modeling Approach of Crack Growth in Materials with Anisotropic Fracture Toughness. In 2nd International Conference of the DFG International Research Training Group 2057 – Physical Modeling for Virtual Manufacturing (iPMVM 2020). Open Access Series in Informatics (OASIcs), Volume 89, pp. 9:1-9:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)
https://doi.org/10.4230/OASIcs.iPMVM.2020.9

## Abstract

Within this contribution, we present a diffuse interface approach for the simulation of crack nucleation and growth in materials, which incorporates an orientation dependency of the fracture toughness. After outlining the basic motivation for the model from an engineering standpoint, the phase field paradigm for fracture is introduced. Further, a specific phase field model for brittle fracture is reviewed, where we focus on the meaning of the auxiliary parameter differentiating between material phases and the coupling of such a parameter to continuum equations in order to obtain the characteristic self organizing model properties. This specific model, as will be explained, provides the phenomenological and methodical basis for the presented enhancement. The formulation of an appropriate evolution equation in terms of a Ginzburg-Landau type equation will be highlighted and several comments on sharp interface models will be made to present a brief comparison. Following up on the basics we then introduce the formulation of a modified version of the model, which additionally to the handling of cracks in linear elastic materials under quasi static loading is also capable of taking into account the effect of resistance variation with respect to the potential crack extension direction. The strong and also the weak forms of the respective governing equations corresponding to the developed anisotropic phase field model are presented. Utilizing the weak formulation as starting point for the discretization of the two fields (displacement field and the phase field), the computational framework in terms of finite elements is introduced. We finally explain several test cases investigated within simulations and discuss the corresponding numerical results. Besides examples, which are set up to illustrate the general model properties, a comparison with crack paths obtained by experimental investigations will be presented in order to show the potential of the developed phase field model.

## Subject Classification

##### ACM Subject Classification
• Applied computing → Physical sciences and engineering
##### Keywords
• Phase field modeling
• Brittle fracture
• Anisotropic fracture toughness
• Finite elements

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## References

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