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

verfasst von

Sanghyun Lee, Mary F. Wheeler, Thomas Wick

Abstract

This paper introduces a novel diffraction based thermo-hydraulic–mechanical (THM) model for fracture propagation using a phase-field fracture (PFF) approach. The key innovation of the THM-PFF model lies in its integrated treatment of four solution variables—displacements, phase-field, pressure, and temperature—each governed by a combination of conservation of momentum (mechanics problem), a variational inequality (constrained minimization problem), mass conservation (pressure problem), and energy conservation (temperature problem). This leads to a new formulation of a coupled variational inequality system. A major advancement is the development of an extended fixed-stress algorithm, where displacements, phase-field, pressures, and temperatures are solved in a staggered sequence. An important aspect of this work is the global coupling of pressures and temperatures across the domain using diffraction systems, with diffraction coefficients defined by material parameters weighted by the diffusive phase-field variable. To ensure robust local mass conservation, we employ enriched Galerkin finite elements (EG) for both pressure and temperature diffraction equations. By enriching the continuous Galerkin basis functions with discontinuous piecewise constants, EG accurately represents solution and parameter discontinuities while preserving local mass and energy conservation—crucial aspects for THM problems and realistic behavior. Moreover, the use of a predictor–corrector local mesh adaptivity scheme is employed, allowing the model to handle small phase-field length-scale parameters while maintaining high numerical accuracy and reasonable computational cost. These new model and algorithmic developments represent significant advances in the field and have been substantiated through rigorous numerical tests.

Organisationseinheit(en)

Institut für Angewandte Mathematik

Externe Organisation(en)

Florida State University
University of Texas at Austin

Typ

Artikel

Journal

International Journal of Heat and Mass Transfer

Band

239

ISSN

0017-9310

Publikationsdatum

13.12.2024

Publikationsstatus

Elektronisch veröffentlicht (E-Pub)

Peer-reviewed

Ja

ASJC Scopus Sachgebiete

Physik der kondensierten Materie, Maschinenbau, Fließ- und Transferprozesse von Flüssigkeiten

Ziele für nachhaltige Entwicklung

SDG 7 – Erschwingliche und saubere Energie

Elektronische Version(en)

https://doi.org/10.1016/j.ijheatmasstransfer.2024.126487 (Zugang: Geschlossen)