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 pressure-sensitive 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.
Highlights
Computational modelling of fracturing in geological materials and porous media has emerged as a field of intensive research in the past years
In order to computationally deal with crack propagation in geological materials and porous media, different numerical approaches may be used, e.g. boundary elements method (BEM) [24,25,26], peridynamics [27, 28], discrete element method (DEM) [29, 30] and extended finite element method (XFEM) [31, 32]
We present an approach for modelling crack propagation in heterogeneous rocks consisting of brittle and elasto-plastic regions
Summary
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. In order to computationally deal with crack propagation in geological materials and porous media, different numerical approaches may be used, e.g. boundary elements method (BEM) [24,25,26], peridynamics [27, 28], discrete element method (DEM) [29, 30] and extended finite element method (XFEM) [31, 32]. We present a multiphase-field model, capable of describing fracture formation processes in heterogeneous multiphase materials, where separate regions of (i) purely brittle and anisotropic material and (ii) frictional and porous material are present. Based on Griffith’s criterion [22, 40], the total free energy functional F of a domain of volume V is given by:
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