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Fracking, i.e. inducing fractures by hydraulic means, is a technique used for extraction of gas and petroleum from rock formations in the subsurface. Thereby a well is stimulated via fractures induced by a pressurized fluid which is injected into the wellbore. This leads to an increased permeability within the deep‐rock formations and finally to an increased flow of petroleum and natural gas out of...
In the last decades the phase‐field approach to fracture [1–3] has gained wide popularity due to advantages such as straight‐forward modeling of complex crack patterns and crack branching while allowing standard finite‐element discretizations. Time‐discrete phase‐field models of brittle fracture are typically formulated in terms of biconvex minimization problems for which a standard monolithic Newton‐Raphson...
This work outlines a rigorous framework for the ductile failure of frictional materials in elastic‐plastic soil mechanics undergoing large strains. Describing soil crack formation can be achieved in a convenient way by recently developed continuum phase field approaches to fracture, which are based on the regularization of sharp crack discontinuities [1]. This avoids the use of complex discretization...
This work outlines a rigorous variational‐based framework for the phase field modeling of fracture in isotropic and anisotropic porous solids undergoing small elastic but large plastic deformations. It extends the recent work [1] to a formulation of porous plasticity with particulate microstructures characterized by spherical pores or by ellipsoidal voids, which additionally undergo a change in size...
This work outlines a rigorous variational-based framework for the phase field modeling of fracture in isotropic porous solids undergoing large elastic–plastic strains. It extends the recent works of Miehe et al., [33,53] to a particular formulation of isotropic porous plasticity. The phase field approach regularizes sharp crack surfaces within a pure continuum setting by a specific gradient damage...
Hydraulic fracturing has led to controversial public debates about its risks due to environmental issues, such as increased seismic activity or drinking water contamination. The technique is primarily used to gain crude oil or natural gas from unconventional wells. To this end, a high pressurized fracking fluid is injected into a wellbore to fracture deep‐rock formations, leading to growing cracks,...
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