Fracture of thermo-elastic solids: phase-field modeling and new results with an efficient monolithic solver

Tushar Kanti Mandal, Vinh Phu Nguyen, Jian-Ying Wu, Chi Nguyen-Thanh, Alban de Vaucorbeil

Research output: Contribution to journalArticleResearchpeer-review

67 Citations (Scopus)


Thermally induced cracking occurs in many engineering problems such as drying shrinkage cracking of concrete, thermal shock induced fracture, micro cracking of two-phase composite materials etc. The computational simulation of such a fracture is complicated, but the use of phase-field models (PFMs) is promising as they can seamlessly model complex crack patterns like branching, merging, and fragmentation by treating the crack discontinuity as thin band of diffuse damage. Despite the success of phase-field models there are two major issues in previous PFMs of thermally induced fracture. Firstly, these models, which are mostly based on a PFM using a simple quadratic degradation function without any user-defined parameters, provide solutions that are sensitive to a length scale. Secondly, they are limited to brittle fracture only. As a solution, we extend the phase-field regularized cohesive zone model (PF-CZM) of Wu [JMPS, 103 (2017)], with a rational degradation function dependent on elasticity and fracture related material parameters, to thermoelastic solids. Furthermore, we present a monolithic BFGS algorithm to solve the three-field (displacements, phase-field and temperature) coupling equations altogether. Multiple thermally induced fracture problems, simulated within the framework of the finite element method, are presented with predictions in good agreement with previous findings and experiments. The proposed model is shown to give better performance in capturing the physics of thermally induced fracture: it provides length scale insensitive responses. And the monolithic solver is 4∼5 times faster than the conventional alternating minimization solver.

Original languageEnglish
Article number113648
Number of pages35
JournalComputer Methods in Applied Mechanics and Engineering
Publication statusPublished - 1 Apr 2021


  • Fracture
  • Gradient-damage model
  • Monolithic solver
  • Phase-field theory
  • Quasi-brittle solids
  • Thermal shock induced fracture

Cite this