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Damage Mechanics Challenge: Predictions based on the phase field fracture model

Y. Navidtehrani, R. Duddu, E. Martínez-Pañeda

TL;DR

This work addresses predictive fracture modeling for rock-like materials within the Damage Mechanics Challenge by applying a phase-field fracture model in the AT2 formulation. The method calibrates four physically meaningful parameters—$E$, $ν$, $G_c$, and $ℓ$ (which fixes $σ_c$)—from a mode I three-point bend, then uses the calibrated model to predict mixed-mode crack paths and surface morphologies in more complex configurations. The authors report remarkable agreement between blind predictions and experimental data across force–displacement curves, crack trajectories (via DIC), and 3D crack morphologies for a gypsum-like material, demonstrating the robustness and mesh-objectivity of the phase-field approach. They also discuss limitations related to material heterogeneity and potential extensions to anisotropic and non-symmetric fracture surfaces, suggesting future challenges to further stress-test phase-field models in geology and engineering contexts.

Abstract

In this work, we describe our contribution to the Purdue-SANDIA-LLNL \emph{Damage Mechanics Challenge}. The phase field fracture model is adopted to blindly estimate the failure characteristics of the challenge test, an unconventional three-point bending experiment on an additively manufactured rock resembling a type of gypsum. The model is formulated in a variationally consistent fashion, incorporating a volumetric-deviatoric strain energy decomposition, and the numerical implementation adopts a monolithic unconditionally stable solution scheme. Our focus is on providing an efficient and simple yet rigorous approach capable of delivering accurate predictions based solely on physical parameters. Model inputs are Young's modulus $E$, Poisson's ratio $ν$, toughness $G_c$ and strength $σ_c$ (as determined by the choice of phase field length scale $\ell$). We show that a single mode I three-point bending test is sufficient to calibrate the model, and that the calibrated model can then reliably predict the force versus displacement responses, crack paths and surface crack morphologies of more intricate three-point bending experiments that are inherently mixed-mode. Importantly, our peak load, crack trajectory and crack surface morphology predictions for the challenge test, submitted before the experimental data was released, show a remarkable agreement with experiments. The characteristics of the challenge, and how changes in these can impact the predictive abilities of phase field fracture models, are also discussed.

Damage Mechanics Challenge: Predictions based on the phase field fracture model

TL;DR

This work addresses predictive fracture modeling for rock-like materials within the Damage Mechanics Challenge by applying a phase-field fracture model in the AT2 formulation. The method calibrates four physically meaningful parameters—, , , and (which fixes )—from a mode I three-point bend, then uses the calibrated model to predict mixed-mode crack paths and surface morphologies in more complex configurations. The authors report remarkable agreement between blind predictions and experimental data across force–displacement curves, crack trajectories (via DIC), and 3D crack morphologies for a gypsum-like material, demonstrating the robustness and mesh-objectivity of the phase-field approach. They also discuss limitations related to material heterogeneity and potential extensions to anisotropic and non-symmetric fracture surfaces, suggesting future challenges to further stress-test phase-field models in geology and engineering contexts.

Abstract

In this work, we describe our contribution to the Purdue-SANDIA-LLNL \emph{Damage Mechanics Challenge}. The phase field fracture model is adopted to blindly estimate the failure characteristics of the challenge test, an unconventional three-point bending experiment on an additively manufactured rock resembling a type of gypsum. The model is formulated in a variationally consistent fashion, incorporating a volumetric-deviatoric strain energy decomposition, and the numerical implementation adopts a monolithic unconditionally stable solution scheme. Our focus is on providing an efficient and simple yet rigorous approach capable of delivering accurate predictions based solely on physical parameters. Model inputs are Young's modulus , Poisson's ratio , toughness and strength (as determined by the choice of phase field length scale ). We show that a single mode I three-point bending test is sufficient to calibrate the model, and that the calibrated model can then reliably predict the force versus displacement responses, crack paths and surface crack morphologies of more intricate three-point bending experiments that are inherently mixed-mode. Importantly, our peak load, crack trajectory and crack surface morphology predictions for the challenge test, submitted before the experimental data was released, show a remarkable agreement with experiments. The characteristics of the challenge, and how changes in these can impact the predictive abilities of phase field fracture models, are also discussed.
Paper Structure (17 sections, 21 equations, 12 figures)

This paper contains 17 sections, 21 equations, 12 figures.

Table of Contents

  1. Introduction
  2. Approach: Phase field fracture modelling
  3. A phase field description of fracture
  4. Background
  5. Balance equations
  6. Numerical implementation
  7. Numerical experiments: defining the boundary value problem
  8. Challenge data, requisitions and characteristics
  9. Computational details
  10. Calibration of the material parameters
  11. Results
  12. Model benchmarking against calibration data
  13. Blind predictions of the challenge test
  14. Summary, conclusions and outlook
  15. Finite element implementation of phase field fracture
  16. ...and 2 more sections

Figures (12)

  • Figure 1: Damage Mechanics Challenge data: calibration and to-be-predicted experiments. The calibration data included force versus displacement measurements for: (a) four three-point bending configurations (of equal dimensions but different notch configurations), (b) unconfined compressive tests, and (c) Brazilian disk tests. Based on this information, participants were asked to blindly estimate the cracking characteristics (peak load, crack trajectory and morphology) of an unconventional three-point bending test with an inclined, unsymmetric notch (d).
  • Figure 1: Assessing the role of the element type: load versus force results for the challenge test, as obtained using tetrahedral and brick elements.
  • Figure 2: Three-point bending tests used for generating calibration data: geometry, dimensions and boundary conditions. The tests included a conventional three-point bending experiment, denoted as HC (a), two tests where the notch was placed eccentric, HB (b) and HA (c), and a fourth experiment where the notch was inclined 45$^\circ$ along the thickness, requiring a 3D analysis, H45 (d).
  • Figure 3: Finite element discretisation of the three-point bending tests used for generating calibration data. The model HC (a) employs a total of 8,888 bi-linear quadrilateral elements, the model HB (b) uses 11,242 bi-linear quadrilateral elements, the model HA (c) uses 14,622 bi-linear quadrilateral elements, and the three-dimensional model H45 employs 1,953,053 linear tetrahedral elements. Since the crack trajectory is not known a priori, the mesh is strategically refined in regions of potential crack growth.
  • Figure 4: Details of the challenge test: (a) Geometry, dimensions and boundary conditions, and (b) finite element discretisation, employing a total of 904,429 linear brick elements.
  • ...and 7 more figures