Numerical Simulation of Crack Propagation in an Anisotropic Medium. Issue 1 (17th December 2018)

• Record Type: Journal Article
• Authors: Bilgen, Carola; Hennig, Paul; Kästner, Markus; Weinberg, Kerstin
• Other Names: Müller G. guestEditor.; Ulbrich M. guestEditor.
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 18:Issue 1(2018)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2018-12-17
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201800308
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: Phase‐field methods have been proven to address the main challenges in fracture mechanics – the identification of crack initiation and the simulation of the unknown crack paths – in an elegant way. This approach has therefore become very popular recently. Our contribution sets the focus on different ways to capture anisotropy in the phase‐field model. In order to deal with the tension‐compression asymmetry in fracture problems, a suitable operator split has to be deduced to take only the tensile deformations, which lead to crack growth, into account. In general, the strain energy function can be written in terms of principal stretches or principal invariants. A comparison of different decompositions is demonstrated in the context of both, finite and linearized strains. Furthermore, energetic and stress based fracture criteria are considered and checked against each other in more detail. Additionally, material anisotropy is examined within the phase‐field approach using an operator‐scaling anisotropic random field to consider the microstructure of the material implicitly.