Open Collections

Chad Landis: Phase-field Modeling of Hydraulic Fracture

Banff International Research Station for Mathematical Innovation and Discovery

In this talk a theoretical framework implementing the phase-field approach to fracture is used to couple the physics of flow through porous media and cracks with the mechanics of fracture. The main modeling challenge addressed in this work, which is a challenge for all diffuse crack representations, is on how to allow for the flow of fluid and the action of fluid pressure on the aggregate within the diffuse damage zone of the cracks. The theory is constructed by presenting the general physical balance laws, postulating a kinematic ansatz for an effective porosity, and conducting a consistent thermodynamic analysis to constrain the constitutive relationships. Constitutive equations that reproduce the desired responses at the various limits of the effective porosity are proposed in order to capture Darcy-type flow in the intact porous medium and Stokes-type flow within open cracks. A finite element formulation for the solution of the governing model equations is presented and discussed. Finally, the theoretical and numerical model is shown to compare favorably to several important analytical solutions. More complex and interesting calculations are also presented to illustrate some of the advantageous features of the approach.

Mathematics; Mechanics of deformable solids; Calculus of variations and optimal control; optimization; Material science

video/mp4

Author affiliation: University of Texas in Austin

2017-02-09

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/59677

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/