Multiphase-field modelling of crack propagation in geological materials and porous media with Drucker-Prager plasticity

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.

A micromechanics-based variational phase-field model for fracture in geomaterials with brittle-tensile and compressive-ductile behavior

“…For instance, a double phase-field model for tensile, shear, and mixed-mode fracture with plasticity was proposed in You et al [86], while other studies [3,87] focus on modeling the brittle-to-ductile transition phenomenon. Phase-field models coupled to frictional plasticity have been further considered in the finite strain setting [3,88], as well as in the context of multiphase materials [89] and fluiddriven fracture [90,91]. Moreover, building upon the phase-field modeling of frictional interfaces [77], Bryant and Sun [92] proposed a model that embeds rate-, size-, and temperature-dependent friction.…”

Study on Stress and Displacement of Axisymmetric Circular Loess Tunnel Surrounding Rock Based on Joint Strength

“…According to the abovementioned results, which include Formulas ( 16), ( 29), (32), (34) and (37), a series of analytical solutions comprises the modified Fenner formula based on joint strength. In this section, the difference between the modified Fenner formula based on joint strength and the modified Fenner formula based on M-C strength [7] for the unlined loess tunnel will be analysed and discussed.…”

“…However, the Drucker-Prager (D-P) strength criterion was put forward to overcome the corner defect in M-C strength in π plane; it is widely used in numerical analysis of geotechnical engineering. Multiphase-field modelling of crack propagation in geological materials and porous media was analysed based on D-P strength criterion [7]. The king of theoretical solutions in tunnel-excavation processes was deduced through the cavity-expansion theory based on the D-P strength criterion [8].…”

Modeling intercalation in cathode materials with phase-field methods: Assumptions and implications using the example of LiFePO4

“…The second approach is the more general multiphase-field framework [8,9,14] based on Allen-Cahn equations for the evolution of non-conserved order parameters in combination with the evolution of diffusional potential based on the grand-chemical potential [29,30]. This framework has been sucessfully combined with elastic driving forces based on jump conditions [31,32] to model martensitic transformations [12], crack propagation [33][34][35] and the evolution of electric field to study electromigration [36]. It has further been shown that grain boundary diffusion [37] as well as the instability leading to phase separation in the miscibility gap [6] can be effectively modelled.…”