Abstract
Phase-field models of fracture allow the prediction of crack propagation and crack patterns. In this contribution, externally driven fracture processes in linear and finite elasticity are investigated. Different approaches to consider pneumatic pressure and materials with non-isotropic crack resistance are studied, combined, and examined in detail. The versatility of the proposed models is proven by a series of numerical simulations in two and three dimensions.
Highlights
The prediction of crack growth and fracture patterns is a central topic of fracture mechanics
Various studies have been made on external load driven fracture, in particular, on hydraulic fracturing where a fluid under high pressure is injected into compressed soil to open cracks
In this work we present a model for pneumatic fracture in solids with non-isotropic fracture resistance
Summary
The prediction of crack growth and fracture patterns is a central topic of fracture mechanics. Ghamgosar et al (2015) suggest to introduce various critical fracture energy densities GcI , GcI I , GcI I I for each rock direction This technique was used in the early phase-field models of Adda-Bedia et al (1999) to capture the preferred direction of crack propagation. In the last years it has been generalized to a Griffith energy tensor or, alternatively, a structural tensor included in the regularized variational phase-field formulation, cf Clayton and Knap (2015), Teichtmeister et al (2017), Liu and Juhre (2018) and Li et al (2015) Such a tensor weights the partial derivatives in different directions separately. Numerical simulations for pressure induced crack growth in materials with layer-wise fracture resistance are presented in Sect.
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