A phase-field formulation for dynamic cohesive fracture
Abstract
We extend a phase-field/gradient damage formulation for cohesive fracture to the dynamic case. The model is characterized by a regularized fracture energy that is linear in the damage field, as well as non-polynomial degradation functions. Two categories of degradation functions are examined, and a process to derive a given degradation function based on a local stress-strain response in the cohesive zone is presented. The resulting model is characterized by a linear elastic regime prior to the onset of damage, and controlled strain-softening thereafter. The governing equations are derived according to macro- and microforce balance theories, naturally accounting for the irreversible nature of the fracture process by introducing suitable constraints for the kinetics of the underlying microstructural changes. The model is complemented by an efficient staggered solution scheme based on an augmented Lagrangian method. Numerical examples demonstrate that the proposed model is a robust and effective method for simulating cohesive crack propagation, with particular emphasis on dynamic fracture.
- Authors:
-
[1];
[1]
- Duke Univ., Durham, NC (United States)
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- Publication Date:
- Research Org.:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)
- OSTI Identifier:
- 1498479
- Alternate Identifier(s):
- OSTI ID: 1636203
- Report Number(s):
- SAND-2018-13647J
Journal ID: ISSN 0045-7825; 670638
- Grant/Contract Number:
- AC04-94AL85000; NA0003525
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Computer Methods in Applied Mechanics and Engineering
- Additional Journal Information:
- Journal Volume: 348; Journal Issue: C; Journal ID: ISSN 0045-7825
- Publisher:
- Elsevier
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 42 ENGINEERING; Phase-field models; Cohesive fracture; Dynamic fracture; Gradient models; Damage
Citation Formats
Geelen, Rudy J. M., Liu, Yingjie, Hu, Tianchen, Tupek, Michael R., and Dolbow, John E. A phase-field formulation for dynamic cohesive fracture. United States: N. p., 2019.
Web. doi:10.1016/j.cma.2019.01.026.
Geelen, Rudy J. M., Liu, Yingjie, Hu, Tianchen, Tupek, Michael R., & Dolbow, John E. A phase-field formulation for dynamic cohesive fracture. United States. https://doi.org/10.1016/j.cma.2019.01.026
Geelen, Rudy J. M., Liu, Yingjie, Hu, Tianchen, Tupek, Michael R., and Dolbow, John E. Tue .
"A phase-field formulation for dynamic cohesive fracture". United States. https://doi.org/10.1016/j.cma.2019.01.026. https://www.osti.gov/servlets/purl/1498479.
@article{osti_1498479,
title = {A phase-field formulation for dynamic cohesive fracture},
author = {Geelen, Rudy J. M. and Liu, Yingjie and Hu, Tianchen and Tupek, Michael R. and Dolbow, John E.},
abstractNote = {We extend a phase-field/gradient damage formulation for cohesive fracture to the dynamic case. The model is characterized by a regularized fracture energy that is linear in the damage field, as well as non-polynomial degradation functions. Two categories of degradation functions are examined, and a process to derive a given degradation function based on a local stress-strain response in the cohesive zone is presented. The resulting model is characterized by a linear elastic regime prior to the onset of damage, and controlled strain-softening thereafter. The governing equations are derived according to macro- and microforce balance theories, naturally accounting for the irreversible nature of the fracture process by introducing suitable constraints for the kinetics of the underlying microstructural changes. The model is complemented by an efficient staggered solution scheme based on an augmented Lagrangian method. Numerical examples demonstrate that the proposed model is a robust and effective method for simulating cohesive crack propagation, with particular emphasis on dynamic fracture.},
doi = {10.1016/j.cma.2019.01.026},
journal = {Computer Methods in Applied Mechanics and Engineering},
number = C,
volume = 348,
place = {United States},
year = {Tue Feb 05 00:00:00 EST 2019},
month = {Tue Feb 05 00:00:00 EST 2019}
}
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Works referenced in this record:
Convergence of a gradient damage model toward a cohesive zone model
journal, January 2011
- Lorentz, Eric; Cuvilliez, S.; Kazymyrenko, K.
- Comptes Rendus Mécanique, Vol. 339, Issue 1
Modelling large crack propagation: from gradient damage to cohesive zone models
journal, July 2012
- Lorentz, Eric; Cuvilliez, Sam; Kazymyrenko, Kyrylo
- International Journal of Fracture, Vol. 178, Issue 1-2
Nonlocal Damage Theory
journal, October 1987
- Pijaudier‐Cabot, Gilles; Bažant, Zdeněk P.
- Journal of Engineering Mechanics, Vol. 113, Issue 10
On gradient-enhanced damage and plasticity models for failure in quasi-brittle and frictional materials
journal, December 1995
- de Borst, R.; Pamin, J.; Peerlings, R. H. J.
- Computational Mechanics, Vol. 17, Issue 1-2
Gradient Enhanced Damage for Quasi-Brittle Materials
journal, October 1996
- Peerlings, R. H. J.; De Borst, R.; Brekelmans, W. A. M.
- International Journal for Numerical Methods in Engineering, Vol. 39, Issue 19
A level set based model for damage growth: The thick level set approach
journal, December 2010
- Moës, N.; Stolz, C.; Bernard, P. -E.
- International Journal for Numerical Methods in Engineering, Vol. 86, Issue 3
Approximation of functional depending on jumps by elliptic functional via t-convergence
journal, December 1990
- Ambrosio, Luigi; Tortorelli, Vincenzo Maria
- Communications on Pure and Applied Mathematics, Vol. 43, Issue 8
Optimal approximations by piecewise smooth functions and associated variational problems
journal, July 1989
- Mumford, David; Shah, Jayant
- Communications on Pure and Applied Mathematics, Vol. 42, Issue 5
Revisiting brittle fracture as an energy minimization problem
journal, August 1998
- Francfort, G. A.; Marigo, J. -J.
- Journal of the Mechanics and Physics of Solids, Vol. 46, Issue 8
Numerical experiments in revisited brittle fracture
journal, April 2000
- Bourdin, B.; Francfort, G. A.; Marigo, J-J.
- Journal of the Mechanics and Physics of Solids, Vol. 48, Issue 4
The Variational Approach to Fracture
journal, March 2008
- Bourdin, Blaise; Francfort, Gilles A.; Marigo, Jean-Jacques
- Journal of Elasticity, Vol. 91, Issue 1-3
A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits
journal, November 2010
- Miehe, Christian; Hofacker, Martina; Welschinger, Fabian
- Computer Methods in Applied Mechanics and Engineering, Vol. 199, Issue 45-48
Thermodynamically consistent phase-field models of fracture: Variational principles and multi-field FE implementations
journal, August 2010
- Miehe, C.; Welschinger, F.; Hofacker, M.
- International Journal for Numerical Methods in Engineering, Vol. 83, Issue 10
Sharp-crack limit of a phase-field model for brittle fracture
journal, November 2013
- da Silva, Milton N.; Duda, Fernando P.; Fried, Eliot
- Journal of the Mechanics and Physics of Solids, Vol. 61, Issue 11
An overview of the modelling of fracture by gradient damage models
journal, October 2016
- Marigo, Jean-Jacques; Maurini, Corrado; Pham, Kim
- Meccanica, Vol. 51, Issue 12
Gradient damage vs phase-field approaches for fracture: Similarities and differences
journal, December 2016
- de Borst, René; Verhoosel, Clemens V.
- Computer Methods in Applied Mechanics and Engineering, Vol. 312
A unified phase-field theory for the mechanics of damage and quasi-brittle failure
journal, June 2017
- Wu, Jian-Ying
- Journal of the Mechanics and Physics of Solids, Vol. 103
A time-discrete model for dynamic fracture based on crack regularization
journal, November 2010
- Bourdin, Blaise; Larsen, Christopher J.; Richardson, Casey L.
- International Journal of Fracture, Vol. 168, Issue 2
A phase-field description of dynamic brittle fracture
journal, April 2012
- Borden, Michael J.; Verhoosel, Clemens V.; Scott, Michael A.
- Computer Methods in Applied Mechanics and Engineering, Vol. 217-220
A phase field model of dynamic fracture: Robust field updates for the analysis of complex crack patterns: A PHASE FIELD MODEL OF DYNAMIC FRACTURE
journal, July 2012
- Hofacker, M.; Miehe, C.
- International Journal for Numerical Methods in Engineering, Vol. 93, Issue 3
Phase field approximation of dynamic brittle fracture
journal, June 2014
- Schlüter, Alexander; Willenbücher, Adrian; Kuhn, Charlotte
- Computational Mechanics, Vol. 54, Issue 5
Gradient damage modeling of brittle fracture in an explicit dynamics context: GRADIENT DAMAGE MODELING OF BRITTLE FRACTURE IN AN EXPLICIT DYNAMICS CONTEXT
journal, May 2016
- Li, Tianyi; Marigo, Jean-Jacques; Guilbaud, Daniel
- International Journal for Numerical Methods in Engineering, Vol. 108, Issue 11
Hyperbolic phase field modeling of brittle fracture: Part I—Theory and simulations
journal, December 2018
- Kamensky, David; Moutsanidis, Georgios; Bazilevs, Yuri
- Journal of the Mechanics and Physics of Solids, Vol. 121
Hyperbolic phase field modeling of brittle fracture: Part II—immersed IGA–RKPM coupling for air-blast–structure interaction
journal, December 2018
- Moutsanidis, Georgios; Kamensky, David; Chen, J. S.
- Journal of the Mechanics and Physics of Solids, Vol. 121
The Thick Level-Set model for dynamic fragmentation
journal, March 2017
- Stershic, Andrew J.; Dolbow, John E.; Moës, Nicolas
- Engineering Fracture Mechanics, Vol. 172
Gradient Damage Models and Their Use to Approximate Brittle Fracture
journal, November 2010
- Pham, Kim; Amor, Hanen; Marigo, Jean-Jacques
- International Journal of Damage Mechanics, Vol. 20, Issue 4
The issues of the uniqueness and the stability of the homogeneous response in uniaxial tests with gradient damage models
journal, June 2011
- Pham, Kim; Marigo, Jean-Jacques; Maurini, Corrado
- Journal of the Mechanics and Physics of Solids, Vol. 59, Issue 6
Phase field modeling of fracture in multi-physics problems. Part II. Coupled brittle-to-ductile failure criteria and crack propagation in thermo-elastic–plastic solids
journal, September 2015
- Miehe, C.; Hofacker, M.; Schänzel, L. -M.
- Computer Methods in Applied Mechanics and Engineering, Vol. 294
Phase field modeling of fracture in multi-physics problems. Part I. Balance of crack surface and failure criteria for brittle crack propagation in thermo-elastic solids
journal, September 2015
- Miehe, Christian; Schänzel, Lisa-Marie; Ulmer, Heike
- Computer Methods in Applied Mechanics and Engineering, Vol. 294
A phase-field formulation for fracture in ductile materials: Finite deformation balance law derivation, plastic degradation, and stress triaxiality effects
journal, December 2016
- Borden, Michael J.; Hughes, Thomas J. R.; Landis, Chad M.
- Computer Methods in Applied Mechanics and Engineering, Vol. 312
Crack nucleation in variational phase-field models of brittle fracture
journal, January 2018
- Tanné, E.; Li, T.; Bourdin, B.
- Journal of the Mechanics and Physics of Solids, Vol. 110
Gradient damage models: Toward full-scale computations
journal, May 2011
- Lorentz, E.; Godard, V.
- Computer Methods in Applied Mechanics and Engineering, Vol. 200, Issue 21-22
A phase-field model for cohesive fracture: A PHASE-FIELD MODEL FOR COHESIVE FRACTURE
journal, July 2013
- Verhoosel, Clemens V.; de Borst, René
- International Journal for Numerical Methods in Engineering, Vol. 96, Issue 1
Yielding of steel sheets containing slits
journal, May 1960
- Dugdale, D. S.
- Journal of the Mechanics and Physics of Solids, Vol. 8, Issue 2
The Mathematical Theory of Equilibrium Cracks in Brittle Fracture
book, January 1962
- Barenblatt, G. I.
- Advances in Applied Mechanics, 55-129
Concrete fracture models: testing and practice
journal, January 2002
- Bažant, Zdeněk P.
- Engineering Fracture Mechanics, Vol. 69, Issue 2
A finite thickness band method for ductile fracture analysis
journal, December 2009
- Huespe, A. E.; Needleman, A.; Oliver, J.
- International Journal of Plasticity, Vol. 25, Issue 12
The cohesive band model: a cohesive surface formulation with stress triaxiality
journal, March 2013
- Remmers, Joris J. C.; Borst, René; Verhoosel, Clemens V.
- International Journal of Fracture, Vol. 181, Issue 2
Regularized formulation of the variational brittle fracture with unilateral contact: Numerical experiments
journal, August 2009
- Amor, Hanen; Marigo, Jean-Jacques; Maurini, Corrado
- Journal of the Mechanics and Physics of Solids, Vol. 57, Issue 8
Comparison of two algorithms for the computation of fourth-order isotropic tensor functions
journal, January 1998
- Miehe, C.
- Computers & Structures, Vol. 66, Issue 1
Algorithms for computation of stresses and elasticity moduli in terms of Seth-Hill's family of generalized strain tensors
journal, April 2001
- Miehe, Christian; Lambrecht, Matthias
- Communications in Numerical Methods in Engineering, Vol. 17, Issue 5
Damage, gradient of damage and principle of virtual power
journal, March 1996
- Frémond, Michel; Nedjar, Boumediene
- International Journal of Solids and Structures, Vol. 33, Issue 8
A multi-field incremental variational framework for gradient-extended standard dissipative solids
journal, April 2011
- Miehe, Christian
- Journal of the Mechanics and Physics of Solids, Vol. 59, Issue 4
Validation simulations for the variational approach to fracture
journal, June 2015
- Mesgarnejad, A.; Bourdin, B.; Khonsari, M. M.
- Computer Methods in Applied Mechanics and Engineering, Vol. 290
A nonlocal damage model for plain concrete consistent with cohesive fracture
journal, June 2017
- Lorentz, Eric
- International Journal of Fracture, Vol. 207, Issue 2
Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements
journal, November 1976
- Hillerborg, A.; Modéer, M.; Petersson, P. -E.
- Cement and Concrete Research, Vol. 6, Issue 6
From the onset of damage to rupture: construction of responses with damage localization for a general class of gradient damage models
journal, December 2011
- Pham, Kim; Marigo, Jean-Jacques
- Continuum Mechanics and Thermodynamics, Vol. 25, Issue 2-4
Numerical implementation of the variational formulation for quasi-static brittle fracture
journal, January 2007
- Bourdin, Blaise
- Interfaces and Free Boundaries
An augmented-Lagrangian method for the phase-field approach for pressurized fractures
journal, April 2014
- Wheeler, M. F.; Wick, T.; Wollner, W.
- Computer Methods in Applied Mechanics and Engineering, Vol. 271
A dissipation-based arc-length method for robust simulation of brittle and ductile failure
journal, February 2009
- Verhoosel, Clemens V.; Remmers, Joris J. C.; Gutiérrez, Miguel A.
- International Journal for Numerical Methods in Engineering, Vol. 77, Issue 9
Concrete fracture prediction using bilinear softening
journal, April 2007
- Roesler, Jeffrey; Paulino, Glaucio H.; Park, Kyoungsoo
- Cement and Concrete Composites, Vol. 29, Issue 4
A new generalized finite element method for two-scale simulations of propagating cohesive fractures in 3-D: A new generalized finite element method for two-scale simulations of propagating cohesive fractures in 3-D
journal, June 2015
- Kim, J.; Duarte, C. A.
- International Journal for Numerical Methods in Engineering, Vol. 104, Issue 13
Dynamic crack propagation based on loss of hyperbolicity and a new discontinuous enrichment
journal, January 2003
- Belytschko, Ted; Chen, Hao; Xu, Jingxiao
- International Journal for Numerical Methods in Engineering, Vol. 58, Issue 12
An experimental investigation into dynamic fracture: III. On steady-state crack propagation and crack branching
journal, October 1984
- Ravi-Chandar, K.; Knauss, W. G.
- International Journal of Fracture, Vol. 26, Issue 2
Explicit dynamics with a non-local damage model using the thick level set approach
journal, December 2014
- Moreau, K.; Moës, N.; Picart, D.
- International Journal for Numerical Methods in Engineering, Vol. 102, Issue 3-4
Cracking node method for dynamic fracture with finite elements
journal, January 2009
- Song, Jeong-Hoon; Belytschko, Ted
- International Journal for Numerical Methods in Engineering, Vol. 77, Issue 3
A continuation method for rigid-cohesive fracture in a discontinuous Galerkin finite element setting
journal, May 2018
- Hirmand, M. Reza; Papoulia, Katerina D.
- International Journal for Numerical Methods in Engineering, Vol. 115, Issue 5
Stochastic finite element with material uncertainties: Implementation in a general purpose simulation program
journal, February 2013
- Shang, Shen; Yun, Gun Jin
- Finite Elements in Analysis and Design, Vol. 64
Approximation of functional depending on jumps by elliptic functional via t-convergence
journal, December 1990
- Ambrosio, Luigi; Tortorelli, Vincenzo Maria
- Communications on Pure and Applied Mathematics, Vol. 43, Issue 8
Dynamic crack propagation based on loss of hyperbolicity and a new discontinuous enrichment
journal, January 2003
- Belytschko, Ted; Chen, Hao; Xu, Jingxiao
- International Journal for Numerical Methods in Engineering, Vol. 58, Issue 12
Yielding of steel sheets containing slits
journal, May 1960
- Dugdale, D. S.
- Journal of the Mechanics and Physics of Solids, Vol. 8, Issue 2
Works referencing / citing this record:
Computational modeling of pitting corrosion
journal, September 2019
- Jafarzadeh, Siavash; Chen, Ziguang; Bobaru, Florin
- Corrosion Reviews, Vol. 37, Issue 5
A phase‐field method for modeling cracks with frictional contact
journal, October 2019
- Fei, Fan; Choo, Jinhyun
- International Journal for Numerical Methods in Engineering, Vol. 121, Issue 4
An adaptive space-time phase field formulation for dynamic fracture of brittle shells based on LR NURBS
journal, January 2020
- Paul, Karsten; Zimmermann, Christopher; Mandadapu, Kranthi K.
- Computational Mechanics, Vol. 65, Issue 4
Discrete and Phase Field Methods for Linear Elastic Fracture Mechanics: A Comparative Study and State-of-the-Art Review
journal, June 2019
- Egger, Adrian; Pillai, Udit; Agathos, Konstantinos
- Applied Sciences, Vol. 9, Issue 12
Discrete and phase field methods for linear elastic fracture mechanics: A comparative study and state-of-the-art review
text, January 2019
- Egger, Adrian; Pillai, Udit; Agathos, Konstantinos
- ETH Zurich
A phase-field method for modeling cracks with frictional contact
text, January 2019
- Fei, Fan; Choo, Jinhyun
- arXiv