## A phase-field model of fracture with frictionless contact and random fracture properties: Application to thin-film fracture and soil desiccation

Publication ,  Journal Article
Hu, T; Guilleminot, J; Dolbow, JE
Published in: Computer Methods in Applied Mechanics and Engineering
August 15, 2020

We present a new derivation for a phase-field model of cohesive fracture that allows for fully-damaged surfaces to properly transmit tractions under frictionless contact conditions. The model is derived from an energy minimization standpoint, and the governing equations are presented in a general Allen–Cahn form, unifying both brittle and cohesive fracture models. A novel elastic energy split is proposed to enforce frictionless contact conditions along the regularized crack set. A fixed-point iterative algorithm is used to solve the system of equations, and an active-set strategy is incorporated to enforce the crack set irreversibility. The model is then applied to study the mechanical-fracture coupling in the fracture of thin films and soil desiccation problems in which intricate crack networks form. We present results for one-dimensional, two-dimensional, and fully three-dimensional configurations, and examine the relationship between the generalized driving energies for fracture and the resulting fracture patterns. We also investigate the impact of stochastic spatial variations in material parameters on fragment statistics and fracture network morphology. To this end, we develop a random field model for fracture properties and address a forward propagation problem. The versatility offered by the probabilistic framework is finally highlighted by considering a statistical inverse problem based on physical experiments. It is shown, in particular, that the formulation allows key characteristics of observed crack patterns to be reproduced with reasonable accuracy.

## Published In

Computer Methods in Applied Mechanics and Engineering

0045-7825

August 15, 2020

## Volume

368

• Applied Mathematics
• 49 Mathematical sciences
• 40 Engineering
• 09 Engineering
• 01 Mathematical Sciences

### Citation

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Hu, T., Guilleminot, J., & Dolbow, J. E. (2020). A phase-field model of fracture with frictionless contact and random fracture properties: Application to thin-film fracture and soil desiccation. Computer Methods in Applied Mechanics and Engineering, 368. https://doi.org/10.1016/j.cma.2020.113106
Hu, T., J. Guilleminot, and J. E. Dolbow. “A phase-field model of fracture with frictionless contact and random fracture properties: Application to thin-film fracture and soil desiccation.” Computer Methods in Applied Mechanics and Engineering 368 (August 15, 2020). https://doi.org/10.1016/j.cma.2020.113106.
Hu T, Guilleminot J, Dolbow JE. A phase-field model of fracture with frictionless contact and random fracture properties: Application to thin-film fracture and soil desiccation. Computer Methods in Applied Mechanics and Engineering. 2020 Aug 15;368.
Hu, T., et al. “A phase-field model of fracture with frictionless contact and random fracture properties: Application to thin-film fracture and soil desiccation.” Computer Methods in Applied Mechanics and Engineering, vol. 368, Aug. 2020. Scopus, doi:10.1016/j.cma.2020.113106.
Hu T, Guilleminot J, Dolbow JE. A phase-field model of fracture with frictionless contact and random fracture properties: Application to thin-film fracture and soil desiccation. Computer Methods in Applied Mechanics and Engineering. 2020 Aug 15;368.

## Published In

Computer Methods in Applied Mechanics and Engineering

0045-7825

August 15, 2020

368