Phase-field computation of brittle fracture: robustness, efficiency, and characterisation of solution non-uniqueness

• Applicants: Professorin Dr. Laura De Lorenzis; Professor Dr. Hermann Georg Matthies
• Subject Area: Mechanics
• Term: from 2018 to 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 328873018

• Final Report Year: 2022

Final Report Abstract

Modelling and accurate prediction of complicated fracture processes in elastic solids including crack initiation, propagation, branching, and coalescence, is a very challenging topic of engineering interest. In this project, we focused on brittle materials where fracture occurs prior to significant plastic (permanent) deformation. The phase-field approach enables realistic simulations of such material failure processes by associating a continuous field (the crack phase-field) to the state of the material, ranging from intact to fully broken. However, phase-field models of fracture may result in mathematically nonunique solutions. To capture and characterize this non-uniqueness, we introduced the concept of stochastic solutions, and computed approximations to them. The final result of the computation is not a single crack pattern, but rather several possible crack patterns and their probabilities. The new stochastic solution framework allows additionally the interesting possibility of conditioning the probabilities of further crack paths on intermediate crack patterns, which can be very useful for engineering purposes. Phase-field models are computationally very demanding, and even more so when stochastic aspects are accounted for. To address this issue, we investigated multi-fidelity methods for the stochastic computations. To this end, we first developed and tested an embedded discontinuity approach for quasi-brittle fracture, which is much faster than the phase-field approach at a slight loss of accuracy. The phase-field and the embedded discontinuity approaches were then coupled with stochastic descriptions and stochastic computational processes in a non-intrusive manner. The multi-fidelity combination of the two approaches holds promise to deliver fast and accurate stochastic computations of brittle fracture, and its full exploitation will be the subject of further research.

Publications

• Stochastic phasefield modeling of brittle fracture: computing multiple crack patterns and their probabilities, Computer Methods in Applied Mechanics and Engineering 372 (2020) 113353
  T Gerasimov, U Römer, J Vondřejc, HG Matthies, and L De Lorenzis
  
• Crack propagation simulation without crack tracking algorithm: embedded discontinuity formulation with incompatible modes, Computer Methods in Applied Mechanics and Engineering 386 (2021) 114090
  A Stanić, B Brank, A Ibrahimbegovic, and HG Matthies
  
• Parameter identification for phasefield modeling of fracture: a Bayesian approach with sampling-free update, Computational Mechanics 67 (2021) 435–453
  Tao Wu, B Rosić, L De Lorenzis, and HG Matthies
  
• Parameter Identification in Dynamic Crack Propagation, University of Sarajevo — Faculty of Civil Engineering, ECCOMAS MSF 2021, pp. 93–95
  A Stanić, M Nikolić, N Friedman, and HG Matthies
  
• Synergy of stochastics and inelasticity at multiple scales: novel Bayesian applications in stochastic upscaling and fracture size and scale effects, Springer Nature Applied Sciences 4 (2022) 191
  A Ibrahimbegovic, HG Matthies, S Dobrilla, E Karavelić, RA Mejia Nava, CU Nguyen, MS Sarfaraz, A Stanić, and J Vondřejc