A Thermo‐Flow‐Mechanics‐Fracture Model Coupling a Phase‐Field Interface Approach and Thermo‐Fluid‐Structure Interaction

Lee, Sanghyun; von Wahl, Henry; Wick, Thomas

doi:10.1002/nme.7646

Title: A Thermo‐Flow‐Mechanics‐Fracture Model Coupling a Phase‐Field Interface Approach and Thermo‐Fluid‐Structure Interaction

Journal Article · 30 December 2024 · International Journal for Numerical Methods in Engineering

DOI: https://doi.org/10.1002/nme.7646 · OSTI ID:2484201

Lee, Sanghyun ^[1];

^[2];

^[3]

Department of Mathematics Florida State University Tallahassee Florida
Fakultät für Mathematik und Informatik Friedrich‐Schiller‐Universität Jena Jena Germany
Institut für Angewandte Mathematik Leibniz Universität Hannover Hannover Germany

ABSTRACT This work proposes a novel approach for coupling non‐isothermal fluid dynamics with fracture mechanics to capture thermal effects within fluid‐filled fractures accurately. This method addresses critical aspects of calculating fracture width in enhanced geothermal systems, where the temperature effects of fractures are crucial. The proposed algorithm features an iterative coupling between an interface‐capturing phase‐field fracture method and interface‐tracking thermo‐fluid‐structure interaction using arbitrary Lagrangian–Eulerian coordinates. We use a phase‐field approach to represent fractures and reconstruct the geometry to frame a thermo‐fluid‐structure interaction problem, resulting in pressure and temperature fields that drive fracture propagation. We developed a novel phase‐field interface model accounting for thermal effects, enabling the coupling of quantities specific to the fluid‐filled fracture with the phase‐field model through the interface between the fracture and the intact solid domain. We provide several numerical examples to demonstrate the capabilities of the proposed algorithm. In particular, we analyze mesh convergence of our phase‐field interface model, investigate the effects of temperature on crack width and volume in a static regime, and highlight the method's potential for modeling slowly propagating fractures.

View Journal Article

Cite

Export

Save

Sponsoring Organization:: USDOE

Grant/Contract Number:: SC0024703

OSTI ID:: 2484201

Journal Information:: International Journal for Numerical Methods in Engineering, Journal Name: International Journal for Numerical Methods in Engineering Journal Issue: 1 Vol. 126; ISSN 0029-5981

Publisher:: Wiley Blackwell (John Wiley & Sons)Copyright Statement

Country of Publication:: United Kingdom

Language:: English

References (50)

Approximation of functional depending on jumps by elliptic functional via t-convergence Ambrosio, Luigi; Tortorelli, Vincenzo Maria Communications on Pure and Applied Mathematics, Vol. 43, Issue 8 https://doi.org/10.1002/cpa.3160430805	journal	December 1990
Modelling crack growth by level sets in the extended finite element method Stolarska, M.; Chopp, D. L.; Moës, N. International Journal for Numerical Methods in Engineering, Vol. 51, Issue 8 https://doi.org/10.1002/nme.201	journal	April 2001
Three-dimensional non-planar crack growth by a coupled extended finite element and fast marching method Sukumar, N.; Chopp, D. L.; Béchet, E. International Journal for Numerical Methods in Engineering, Vol. 76, Issue 5 https://doi.org/10.1002/nme.2344	journal	October 2008
Thermodynamically consistent phase-field models of fracture: Variational principles and multi-field FE implementations Miehe, C.; Welschinger, F.; Hofacker, M. International Journal for Numerical Methods in Engineering, Vol. 83, Issue 10 https://doi.org/10.1002/nme.2861	journal	August 2010
The extended/generalized finite element method: An overview of the method and its applications Fries, Thomas-Peter; Belytschko, Ted International Journal for Numerical Methods in Engineering https://doi.org/10.1002/nme.2914	journal	January 2010
CutFEM: Discretizing geometry and partial differential equations: DISCRETIZING GEOMETRY AND PARTIAL DIFFERENTIAL EQUATIONS Burman, Erik; Claus, Susanne; Hansbo, Peter International Journal for Numerical Methods in Engineering, Vol. 104, Issue 7 https://doi.org/10.1002/nme.4823	journal	December 2014
Coupled thermo‐mechanical algorithm for fractured rock mass by the composite element method Xue, Luan‐Luan; Ni, Jia; Wang, Lin‐Wei International Journal for Numerical Methods in Engineering, Vol. 121, Issue 21 https://doi.org/10.1002/nme.6492	journal	July 2020
Modeling non‐isothermal two‐phase fluid flow with phase change in deformable fractured porous media using extended finite element method Khoei, Amir R.; Amini, Danial; Mortazavi, S. Mohammad S. International Journal for Numerical Methods in Engineering, Vol. 122, Issue 16 https://doi.org/10.1002/nme.6709	journal	May 2021
Reconstruct lower‐dimensional crack paths from phase‐field point cloud Xu, Yue; You, Tao; Zhu, Qizhi International Journal for Numerical Methods in Engineering, Vol. 124, Issue 15 https://doi.org/10.1002/nme.7249	journal	April 2023
A novel phase‐field monolithic scheme for brittle crack propagation based on the limited‐memory BFGS method with adaptive mesh refinement Jin, Tao; Li, Zhao; Chen, Kuiying International Journal for Numerical Methods in Engineering https://doi.org/10.1002/nme.7572	journal	July 2024
New crack-tip elements for XFEM and applications to cohesive cracks Zi, Goangseup; Belytschko, Ted International Journal for Numerical Methods in Engineering, Vol. 57, Issue 15 https://doi.org/10.1002/nme.849	journal	January 2003
Stationary Solutions for Generalized Boussinesq Models Lorca, Sebastián A.; Boldrini, José Luiz Journal of Differential Equations, Vol. 124, Issue 2 https://doi.org/10.1006/jdeq.1996.0016	journal	January 1996
Crack opening displacement and the rate of fatigue crack growth Donahue, R. J.; Clark, H. McI; Atanmo, P. International Journal of Fracture Mechanics, Vol. 8, Issue 2 https://doi.org/10.1007/BF00703882	journal	June 1972
NETGEN An advancing front 2D/3D-mesh generator based on abstract rules Schöberl, Joachim Computing and Visualization in Science, Vol. 1, Issue 1 https://doi.org/10.1007/s007910050004	journal	July 1997
Iterative coupling of flow, geomechanics and adaptive phase-field fracture including level-set crack width approaches Lee, Sanghyun; Wheeler, Mary F.; Wick, Thomas Journal of Computational and Applied Mathematics, Vol. 314 https://doi.org/10.1016/j.cam.2016.10.022	journal	April 2017
A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits Miehe, Christian; Hofacker, Martina; Welschinger, Fabian Computer Methods in Applied Mechanics and Engineering, Vol. 199, Issue 45-48 https://doi.org/10.1016/j.cma.2010.04.011	journal	November 2010
Finite elements for fluid–structure interaction in ALE and fully Eulerian coordinates Richter, Th.; Wick, Th. Computer Methods in Applied Mechanics and Engineering, Vol. 199, Issue 41-44 https://doi.org/10.1016/j.cma.2010.04.016	journal	October 2010
A phase-field description of dynamic brittle fracture Borden, Michael J.; Verhoosel, Clemens V.; Scott, Michael A. Computer Methods in Applied Mechanics and Engineering, Vol. 217-220 https://doi.org/10.1016/j.cma.2012.01.008	journal	April 2012
A primal-dual active set method and predictor-corrector mesh adaptivity for computing fracture propagation using a phase-field approach Heister, Timo; Wheeler, Mary F.; Wick, Thomas Computer Methods in Applied Mechanics and Engineering, Vol. 290 https://doi.org/10.1016/j.cma.2015.03.009	journal	June 2015
Phase-field modeling of proppant-filled fractures in a poroelastic medium Lee, Sanghyun; Mikelić, Andro; Wheeler, Mary F. Computer Methods in Applied Mechanics and Engineering, Vol. 312 https://doi.org/10.1016/j.cma.2016.02.008	journal	December 2016
Pressure and fluid-driven fracture propagation in porous media using an adaptive finite element phase field model Lee, Sanghyun; Wheeler, Mary F.; Wick, Thomas Computer Methods in Applied Mechanics and Engineering, Vol. 305 https://doi.org/10.1016/j.cma.2016.02.037	journal	June 2016
A variational phase-field model for hydraulic fracturing in porous media Chukwudozie, Chukwudi; Bourdin, Blaise; Yoshioka, Keita Computer Methods in Applied Mechanics and Engineering, Vol. 347 https://doi.org/10.1016/j.cma.2018.12.037	journal	April 2019
A phase-field description for pressurized and non-isothermal propagating fractures Noii, Nima; Wick, Thomas Computer Methods in Applied Mechanics and Engineering, Vol. 351 https://doi.org/10.1016/j.cma.2019.03.058	journal	July 2019
IPACS: Integrated Phase-Field Advanced Crack Propagation Simulator. An adaptive, parallel, physics-based-discretization phase-field framework for fracture propagation in porous media Wheeler, Mary F.; Wick, Thomas; Lee, Sanghyun Computer Methods in Applied Mechanics and Engineering, Vol. 367 https://doi.org/10.1016/j.cma.2020.113124	journal	August 2020
On crack opening computation in variational phase-field models for fracture Yoshioka, Keita; Naumov, Dmitri; Kolditz, Olaf Computer Methods in Applied Mechanics and Engineering, Vol. 369 https://doi.org/10.1016/j.cma.2020.113210	journal	September 2020
Asynchronous phase field fracture model for porous media with thermally non-equilibrated constituents Suh, Hyoung Suk; Sun, WaiChing Computer Methods in Applied Mechanics and Engineering, Vol. 387 https://doi.org/10.1016/j.cma.2021.114182	journal	December 2021
A modified combined active-set Newton method for solving phase-field fracture into the monolithic limit Kolditz, Leon; Mang, Katrin; Wick, Thomas Computer Methods in Applied Mechanics and Engineering, Vol. 414 https://doi.org/10.1016/j.cma.2023.116170	journal	September 2023
A high-accuracy framework for phase-field fracture interface reconstructions with application to Stokes fluid-filled fracture surrounded by an elastic medium von Wahl, Henry; Wick, Thomas Computer Methods in Applied Mechanics and Engineering, Vol. 415 https://doi.org/10.1016/j.cma.2023.116202	journal	October 2023
A phase-field fracture model in thermo-poro-elastic media with micromechanical strain energy degradation Liu, Yuhao; Yoshioka, Keita; You, Tao Computer Methods in Applied Mechanics and Engineering, Vol. 429 https://doi.org/10.1016/j.cma.2024.117165	journal	September 2024
A continuum phase field model for fracture Kuhn, Charlotte; Müller, Ralf Engineering Fracture Mechanics, Vol. 77, Issue 18 https://doi.org/10.1016/j.engfracmech.2010.08.009	journal	December 2010
Modeling of hydraulic fracturing using a porous-media phase-field approach with reference to experimental data Heider, Yousef; Reiche, Sönke; Siebert, Philipp Engineering Fracture Mechanics, Vol. 202 https://doi.org/10.1016/j.engfracmech.2018.09.010	journal	October 2018
A review on phase-field modeling of hydraulic fracturing Heider, Yousef Engineering Fracture Mechanics, Vol. 253 https://doi.org/10.1016/j.engfracmech.2021.107881	journal	August 2021
Evolution of fracture permeability through fluid–rock reaction under hydrothermal conditions Yasuhara, H.; Polak, A.; Mitani, Y. Earth and Planetary Science Letters, Vol. 244, Issue 1-2 https://doi.org/10.1016/j.epsl.2006.01.046	journal	April 2006
Experimental investigation of fracture aperture and permeability change within Enhanced Geothermal Systems Caulk, Robert A.; Ghazanfari, Ehsan; Perdrial, Julia N. Geothermics, Vol. 62 https://doi.org/10.1016/j.geothermics.2016.02.003	journal	July 2016
Buoyancy-driven flows beyond the Boussinesq approximation: A brief review Mayeli, Peyman; Sheard, Gregory J. International Communications in Heat and Mass Transfer, Vol. 125 https://doi.org/10.1016/j.icheatmasstransfer.2021.105316	journal	June 2021
A phase-field diffraction model for thermo-hydro-mechanical propagating fractures Lee, Sanghyun; Wheeler, Mary F.; Wick, Thomas International Journal of Heat and Mass Transfer, Vol. 239 https://doi.org/10.1016/j.ijheatmasstransfer.2024.126487	journal	April 2025
Analysis of thermally induced changes in fractured rock permeability during 8 years of heating and cooling at the Yucca Mountain Drift Scale Test Rutqvist, J.; Freifeld, B.; Min, K. -B. International Journal of Rock Mechanics and Mining Sciences, Vol. 45, Issue 8 https://doi.org/10.1016/j.ijrmms.2008.01.016	journal	December 2008
An investigation of stimulation mechanisms in Enhanced Geothermal Systems McClure, Mark W.; Horne, Roland N. International Journal of Rock Mechanics and Mining Sciences, Vol. 72 https://doi.org/10.1016/j.ijrmms.2014.07.011	journal	December 2014
High-accuracy phase-field models for brittle fracture based on a new family of degradation functions Sargado, Juan Michael; Keilegavlen, Eirik; Berre, Inga Journal of the Mechanics and Physics of Solids, Vol. 111 https://doi.org/10.1016/j.jmps.2017.10.015	journal	February 2018
Thermal effects on fracture toughness of cracked straight-through Brazilian disk green sandstone and granite Zhou, Lei; Gao, Weiting; Yu, Liyuan Journal of Rock Mechanics and Geotechnical Engineering, Vol. 14, Issue 5 https://doi.org/10.1016/j.jrmge.2022.02.016	journal	October 2022
Stability analysis of the phase-field method for fracture with a general degradation function and plasticity induced crack generation Arriaga, Miguel; Waisman, Haim Mechanics of Materials, Vol. 116 https://doi.org/10.1016/j.mechmat.2017.04.003	journal	January 2018
A coupled high-accuracy phase-field fluid–structure interaction framework for Stokes fluid-filled fracture surrounded by an elastic medium von Wahl, Henry; Wick, Thomas Results in Applied Mathematics, Vol. 22 https://doi.org/10.1016/j.rinam.2024.100455	journal	May 2024
Enhanced geothermal systems (EGS): A review Olasolo, P.; Juárez, M. C.; Morales, M. P. Renewable and Sustainable Energy Reviews, Vol. 56 https://doi.org/10.1016/j.rser.2015.11.031	journal	April 2016
A global review of enhanced geothermal system (EGS) Lu, Shyi-Min Renewable and Sustainable Energy Reviews, Vol. 81 https://doi.org/10.1016/j.rser.2017.06.097	journal	January 2018
Thermal effect on the fracture behavior of granite using acoustic emission and digital image correlation: An experimental investigation Zhang, Xin; Li, Zhonghui; Wang, Xiaoran Theoretical and Applied Fracture Mechanics, Vol. 121 https://doi.org/10.1016/j.tafmec.2022.103540	journal	October 2022
Permeability reduction in granite under hydrothermal conditions Morrow, C. A.; Moore, D. E.; Lockner, D. A. Journal of Geophysical Research: Solid Earth, Vol. 106, Issue B12 https://doi.org/10.1029/2000JB000010	journal	December 2001
The distribution of stress in the neighbourhood of a crack in an elastic solid Sneddon, Ian Naismith Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, Vol. 187, Issue 1009, p. 229-260 https://doi.org/10.1098/rspa.1946.0077	journal	October 1946
An Error-Oriented Newton/Inexact Augmented Lagrangian Approach for Fully Monolithic Phase-Field Fracture Propagation Wick, Thomas SIAM Journal on Scientific Computing, Vol. 39, Issue 4 https://doi.org/10.1137/16m1063873	journal	January 2017
The crack opening displacement approach to fracture mechanics in yielding materials Burdekin, F. M.; Stone, D. E. W. Journal of Strain Analysis, Vol. 1, Issue 2 https://doi.org/10.1243/03093247V012145	journal	January 1966
ngsxfem: Add-on to NGSolve for geometrically unfitted finite element discretizations Lehrenfeld, Christoph; Heimann, Fabian; Preuß, Janosch Journal of Open Source Software, Vol. 6, Issue 64 https://doi.org/10.21105/joss.03237	journal	August 2021

Similar Records

A phase-field diffraction model for thermo-hydro-mechanical propagating fractures

Journal Article · 2024 · International Journal of Heat and Mass Transfer · OSTI ID:2571747

Lee, Sanghyun; Wheeler, Mary F.; Wick, Thomas

New self-consistent homogenization for thermo-elastic polycrystals with imperfect interfaces

Journal Article · 2020 · Mechanics of Materials · OSTI ID:1726215

Zecevic, Miroslav; Bennett, Kane; Luscher, Darby Jon; +1 more

A coupled thermo-hydro-mechanical model for simulating leakoff-dominated hydraulic fracturing with application to geologic carbon storage

Journal Article · 2021 · International Journal of Greenhouse Gas Control · OSTI ID:1833204

Ju, Xin; Fu, Pengcheng; Settegast, Randolph R.; +1 more

Title: A Thermo‐Flow‐Mechanics‐Fracture Model Coupling a Phase‐Field Interface Approach and Thermo‐Fluid‐Structure Interaction

Citation Formats

References (50)

Similar Records

Related Subjects