Multiphase-field modelling of crack propagation in geological materials and porous media with Drucker-Prager plasticity
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ORIGINAL PAPER
Multiphase-field modelling of crack propagation in geological materials and porous media with Drucker-Prager plasticity ¨ 1 · Christoph Herrmann1 · Nishant Prajapati1 · Daniel Schneider1,2 · Felix Schwab1 · Michael Spath Michael Selzer1,2 · Britta Nestler1,2 Received: 24 July 2019 / Accepted: 22 September 2020 © The Author(s) 2020
Abstract A multiphase-field approach for elasto-plastic and anisotropic brittle crack propagation in geological systems consisting of different regions of brittle and ductile materials is presented and employed to computationally study crack propagation. Plastic deformation in elasto-plastic materials such as frictional, granular or porous materials is modelled with the pressuresensitive Drucker-Prager plasticity model. This plasticity model is combined with a multiphase-field model fulfilling the mechanical jump conditions in diffuse solid-solid interfaces. The validity of the plasticity model with phase-inherent stress and strain fields is shown, in comparison with sharp interface finite element solutions. The proposed model is capable of simulating crack formation in heterogeneous multiphase systems comprising both purely elastic and inelastic phases. We investigate the influence of different material parameters on the crack propagation with tensile tests in single- and two-phase materials. To show the applicability of the model, crack propagation in a multiphase domain with brittle and elasto-plastic components is performed. Keywords Multiphase-field · Drucker-Prager plasticity · Brittle fracture · Elasto-plastic fracture
1 Introduction Computational modelling of fracturing in geological materials and porous media (e.g. sands, rocks or clay) has emerged as a field of intensive research in the past years. Predictive investigations of crack-induced failure play a crucial role in rock engineering applications such as underground excavation, rock cutting, hydrofracturing and rock stability [1]. In production engineering, fracture mechanics approaches assist in understanding the stress states and mechanical behaviour of naturally fractured reservoir systems [2]. Crack propagation in sedimentary rocks (e.g. sandstones) is a complex phenomenon due to the presence of physical inhomogeneities at grain scale along with pre-existing Michael Sp¨ath
[email protected] 1
Institute of Applied Materials (IAM-CMS), Karlsruhe Institute of Technology (KIT), Strasse am Forum 7, 76131, Karlsruhe, Germany
2
Institute of Digital Materials Science (IDM), Karlsruhe University of Applied Sciences, Moltkestrasse 30, 76133, Karlsruhe, Germany
fractures which impact the strength and other mechanical properties of these rocks [3–5]. There is an extensive literature of experiments dealing with crack initiation, propagation and coalescence in rocks or rock-like materials under different loading conditions [6–13]. Depending upon the geophysical factors (e.g. pressure, temperature, mineralogy, strain rates and grain size), different rocks exhibit diverse modes of failure, ranging from linea
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