Fragmentation analysis of a bar with the Lip-field approach

Moës, Nicolas; Lé, Benoît; Stershic, Andrew

doi:10.1016/j.mechmat.2022.104365

Fragmentation analysis of a bar with the Lip-field approach

Journal Article · Sat May 28 00:00:00 EDT 2022 · Mechanics of Materials

DOI:https://doi.org/10.1016/j.mechmat.2022.104365· OSTI ID:1883189

Moës, Nicolas ^[1]; Lé, Benoît ^[2]; ^[3]

Ecole Centrale Nantes (France); Institut Univ. de France (IUF), Paris (France)
Ecole Centrale Nantes (France)
Sandia National Lab. (SNL-CA), Livermore, CA (United States)

The Lip-field approach was introduced in Moës and Chevaugeon (2021) as a new way to regularize softening material models. It was tested in 1D quasistatic in Moës and Chevaugeon (2021) and 2D quasistatic in Chevaugeon and Moës (2021): this paper extends it to 1D dynamics, on the challenging problem of dynamic fragmentation. The Lip-field approach formulates the mechanical problem to be solved as an optimization problem, where the incremental potential to be minimized is the non-regularized one. Spurious localization is prevented by imposing a Lipschitz constraint on the damage field. Here, the displacement and damage field at each time step are obtained by a staggered algorithm, that is the displacement field is computed for a fixed damage field, then the damage field is computed for a fixed displacement field. Indeed, these two problems are convex, which is not the case of the global problem where the displacement and damage fields are sought at the same time. The incremental potential is obtained by equivalence with a cohesive zone model, which makes material parameters calibration simple. A non-regularized local damage equivalent to a cohesive zone model is also proposed. It is used as a reference for the Lip-field approach, without the need to implement displacement jumps. These approaches are applied to the brittle fragmentation of a 1D bar with randomly perturbed material properties to accelerate spatial convergence. Both explicit and implicit dynamic implementations are compared. Favorable comparison to several analytical, numerical and experimental references serves to validate the modeling approach.

View Accepted Manuscript (DOE)

Research Organization:: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: NA0003525

OSTI ID:: 1883189

Alternate ID(s):: OSTI ID: 1871767

Report Number(s):: SAND2022-6656J; 706282

Journal Information:: Mechanics of Materials, Journal Name: Mechanics of Materials Vol. 172; ISSN 0167-6636

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (62)

Gradient Enhanced Damage for Quasi-Brittle Materials Peerlings, R. H. J.; De Borst, R.; Brekelmans, W. A. M. International Journal for Numerical Methods in Engineering, Vol. 39, Issue 19 https://doi.org/10.1002/(SICI)1097-0207(19961015)39:19<3391::AID-NME7>3.0.CO;2-D	journal	October 1996
Slope constrained topology optimization Petersson, Joakim; Sigmund, Ole International Journal for Numerical Methods in Engineering, Vol. 41, Issue 8 https://doi.org/10.1002/(SICI)1097-0207(19980430)41:8<1417::AID-NME344>3.0.CO;2-N	journal	April 1998
Peridynamics simulations of geomaterial fragmentation by impulse loads: Peridynamics simulations of geomaterial fragmentation by impulse loads Lai, Xin; Ren, Bo; Fan, Houfu International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 39, Issue 12 https://doi.org/10.1002/nag.2356	journal	March 2015
Cracking particles: a simplified meshfree method for arbitrary evolving cracks Rabczuk, T.; Belytschko, T. International Journal for Numerical Methods in Engineering, Vol. 61, Issue 13 https://doi.org/10.1002/nme.1151	journal	January 2004
The cohesive element approach to dynamic fragmentation: the question of energy convergence Molinari, J. F.; Gazonas, G.; Raghupathy, R. International Journal for Numerical Methods in Engineering, Vol. 69, Issue 3 https://doi.org/10.1002/nme.1777	journal	January 2006
Thermodynamically consistent phase-field models of fracture: Variational principles and multi-field FE implementations Miehe, C.; Welschinger, F.; Hofacker, M. International Journal for Numerical Methods in Engineering, Vol. 83, Issue 10 https://doi.org/10.1002/nme.2861	journal	August 2010
A level set based model for damage growth: The thick level set approach Moës, N.; Stolz, C.; Bernard, P. -E. International Journal for Numerical Methods in Engineering, Vol. 86, Issue 3 https://doi.org/10.1002/nme.3069	journal	December 2010
A phase-field model for cohesive fracture: A PHASE-FIELD MODEL FOR COHESIVE FRACTURE Verhoosel, Clemens V.; de Borst, René International Journal for Numerical Methods in Engineering, Vol. 96, Issue 1 https://doi.org/10.1002/nme.4553	journal	July 2013
Explicit dynamics with a non-local damage model using the thick level set approach Moreau, K.; Moës, N.; Picart, D. International Journal for Numerical Methods in Engineering, Vol. 102, Issue 3-4 https://doi.org/10.1002/nme.4824	journal	December 2014
A cohesive finite element for quasi-continua Liu, Xiaohu; Li, Shaofan; Sheng, Ni Computational Mechanics, Vol. 42, Issue 4 https://doi.org/10.1007/s00466-007-0222-6	journal	October 2007
An embedded atom hyperelastic constitutive model and multiscale cohesive finite element method He, Minghua; Li, Shaofan Computational Mechanics, Vol. 49, Issue 3 https://doi.org/10.1007/s00466-011-0643-0	journal	September 2011
Implementation of Smoothed Particle Hydrodynamics for Detonation of Explosive with Application to Rock Fragmentation Pramanik, R.; Deb, D. Rock Mechanics and Rock Engineering, Vol. 48, Issue 4 https://doi.org/10.1007/s00603-014-0657-y	journal	September 2014
Effects of material properties on the fragmentation of brittle materials Zhou, Fenghua; Molinari, Jean-François; Ramesh, K. T. International Journal of Fracture, Vol. 139, Issue 2 https://doi.org/10.1007/s10704-006-7135-9	journal	May 2006
A new model of damage: a moving thick layer approach Stolz, Claude; Moës, Nicolas International Journal of Fracture, Vol. 174, Issue 1 https://doi.org/10.1007/s10704-012-9693-3	journal	March 2012
On use of the thick level set method in 3D quasi-static crack simulation of quasi-brittle material Salzman, Alexis; Moës, Nicolas; Chevaugeon, Nicolas International Journal of Fracture, Vol. 202, Issue 1 https://doi.org/10.1007/s10704-016-0132-8	journal	August 2016
Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements Hillerborg, A.; Modéer, M.; Petersson, P. -E. Cement and Concrete Research, Vol. 6, Issue 6 https://doi.org/10.1016/0008-8846(76)90007-7	journal	November 1976
Localization limiters in transient problems Lasry, David; Belytschko, Ted International Journal of Solids and Structures, Vol. 24, Issue 6 https://doi.org/10.1016/0020-7683(88)90059-5	journal	January 1988
Computational modelling of impact damage in brittle materials Camacho, G. T.; Ortiz, M. International Journal of Solids and Structures, Vol. 33, Issue 20-22 https://doi.org/10.1016/0020-7683(95)00255-3	journal	August 1996
Yielding of steel sheets containing slits Dugdale, D. S. Journal of the Mechanics and Physics of Solids, Vol. 8, Issue 2 https://doi.org/10.1016/0022-5096(60)90013-2	journal	May 1960
Material rate dependence and mesh sensitivity in localization problems Needleman, A. Computer Methods in Applied Mechanics and Engineering, Vol. 67, Issue 1 https://doi.org/10.1016/0045-7825(88)90069-2	journal	March 1988
Extended finite element method for cohesive crack growth Moës, Nicolas; Belytschko, Ted Engineering Fracture Mechanics, Vol. 69, Issue 7 https://doi.org/10.1016/S0013-7944(01)00128-X	journal	May 2002
Numerical analysis of high speed concrete fragmentation using a meshfree Lagrangian method Rabczuk, Timon; Eibl, Josef; Stempniewski, Lothar Engineering Fracture Mechanics, Vol. 71, Issue 4-6 https://doi.org/10.1016/S0013-7944(03)00032-8	journal	March 2004
Damage model with delay effect Suffis, Arnaud; Lubrecht, Ton A. A.; Combescure, Alain International Journal of Solids and Structures, Vol. 40, Issue 13-14 https://doi.org/10.1016/S0020-7683(03)00153-7	journal	June 2003
Nonlocal models for damage and fracture: Comparison of approaches Jirásek, Milan International Journal of Solids and Structures, Vol. 35, Issue 31-32 https://doi.org/10.1016/S0020-7683(97)00306-5	journal	November 1998
Dynamic fragmentation of brittle materials: analytical mechanics-based models Drugan, W. J. Journal of the Mechanics and Physics of Solids, Vol. 49, Issue 6 https://doi.org/10.1016/S0022-5096(01)00002-3	journal	June 2001
Numerical simulation of crack growth in an isotropic solid with randomized internal cohesive bonds Gao, Huajian; Klein, Patrick Journal of the Mechanics and Physics of Solids, Vol. 46, Issue 2 https://doi.org/10.1016/S0022-5096(97)00047-1	journal	February 1998
Revisiting brittle fracture as an energy minimization problem Francfort, G. A.; Marigo, J. -J. Journal of the Mechanics and Physics of Solids, Vol. 46, Issue 8 https://doi.org/10.1016/S0022-5096(98)00034-9	journal	August 1998
A study of fragmentation processes using a discrete element method Kun, Ferenc; Herrmann, Hans J. Computer Methods in Applied Mechanics and Engineering, Vol. 138, Issue 1-4 https://doi.org/10.1016/S0045-7825(96)01012-2	journal	December 1996
A damage model for the dynamic fragmentation of brittle solids Denoual, Christophe; Hild, François Computer Methods in Applied Mechanics and Engineering, Vol. 183, Issue 3-4 https://doi.org/10.1016/S0045-7825(99)00221-2	journal	March 2000
Physics-based modeling of brittle fracture: cohesive formulations and the application of meshfree methods Klein, P. A.; Foulk, J. W.; Chen, E. P. Theoretical and Applied Fracture Mechanics, Vol. 37, Issue 1-3 https://doi.org/10.1016/S0167-8442(01)00091-X	journal	December 2001
One-dimensional localisation studied with a second grade model Chambon, R.; Caillerie, D.; El Hassan, N. European Journal of Mechanics - A/Solids, Vol. 17, Issue 4 https://doi.org/10.1016/S0997-7538(99)80026-6	journal	July 1998
A scalable 3D fracture and fragmentation algorithm based on a hybrid, discontinuous Galerkin, cohesive element method Radovitzky, R.; Seagraves, A.; Tupek, M. Computer Methods in Applied Mechanics and Engineering, Vol. 200, Issue 1-4 https://doi.org/10.1016/j.cma.2010.08.014	journal	January 2011
A phase-field description of dynamic brittle fracture Borden, Michael J.; Verhoosel, Clemens V.; Scott, Michael A. Computer Methods in Applied Mechanics and Engineering, Vol. 217-220 https://doi.org/10.1016/j.cma.2012.01.008	journal	April 2012
Damage growth modeling using the Thick Level Set (TLS) approach: Efficient discretization for quasi-static loadings Bernard, P. E.; Moës, N.; Chevaugeon, N. Computer Methods in Applied Mechanics and Engineering, Vol. 233-236 https://doi.org/10.1016/j.cma.2012.02.020	journal	August 2012
A geometrically regularized gradient-damage model with energetic equivalence Wu, Jian-Ying Computer Methods in Applied Mechanics and Engineering, Vol. 328 https://doi.org/10.1016/j.cma.2017.09.027	journal	January 2018
A phase-field formulation for dynamic cohesive fracture Geelen, Rudy J. M.; Liu, Yingjie; Hu, Tianchen Computer Methods in Applied Mechanics and Engineering, Vol. 348 https://doi.org/10.1016/j.cma.2019.01.026	journal	May 2019
A phase-field model of fracture with frictionless contact and random fracture properties: Application to thin-film fracture and soil desiccation Hu, Tianchen; Guilleminot, Johann; Dolbow, John E. Computer Methods in Applied Mechanics and Engineering, Vol. 368 https://doi.org/10.1016/j.cma.2020.113106	journal	August 2020
Attaining regularization length insensitivity in phase-field models of ductile failure Talamini, Brandon; Tupek, Michael R.; Stershic, Andrew J. Computer Methods in Applied Mechanics and Engineering, Vol. 384 https://doi.org/10.1016/j.cma.2021.113936	journal	October 2021
An explicit phase field method for brittle dynamic fracture Ren, H. L.; Zhuang, X. Y.; Anitescu, C. Computers & Structures, Vol. 217 https://doi.org/10.1016/j.compstruc.2019.03.005	journal	June 2019
Delay-active damage versus non-local enhancement for anisotropic damage dynamics computations with alternated loading Desmorat, R.; Chambart, M.; Gatuingt, F. Engineering Fracture Mechanics, Vol. 77, Issue 12 https://doi.org/10.1016/j.engfracmech.2010.04.006	journal	August 2010
The Thick Level-Set model for dynamic fragmentation Stershic, Andrew J.; Dolbow, John E.; Moës, Nicolas Engineering Fracture Mechanics, Vol. 172 https://doi.org/10.1016/j.engfracmech.2016.12.012	journal	March 2017
Coupling damage and cohesive zone models with the Thick Level Set approach to fracture Lé, Benoît; Moës, Nicolas; Legrain, Grégory Engineering Fracture Mechanics, Vol. 193 https://doi.org/10.1016/j.engfracmech.2017.12.036	journal	April 2018
Ceramic nuclear fuel fracture modeling with the extended finite element method Jiang, Wen; Spencer, Benjamin W.; Dolbow, John E. Engineering Fracture Mechanics, Vol. 223 https://doi.org/10.1016/j.engfracmech.2019.106713	journal	January 2020
A statistics and energy based theory of dynamic fragmentation Grady, D. E.; Olsen, M. L. International Journal of Impact Engineering, Vol. 29, Issue 1-10 https://doi.org/10.1016/j.ijimpeng.2003.09.026	journal	December 2003
Semi-Lagrangian reproducing kernel particle method for fragment-impact problems Guan, P. C.; Chi, S. W.; Chen, J. S. International Journal of Impact Engineering, Vol. 38, Issue 12 https://doi.org/10.1016/j.ijimpeng.2011.08.001	journal	December 2011
Micro-cracks informed damage models for brittle solids Ren, Xiaodan; Chen, Jiun-Shyan; Li, Jie International Journal of Solids and Structures, Vol. 48, Issue 10 https://doi.org/10.1016/j.ijsolstr.2011.02.001	journal	May 2011
Stress-based nonlocal damage model Giry, Cédric; Dufour, Frédéric; Mazars, Jacky International Journal of Solids and Structures, Vol. 48, Issue 25-26 https://doi.org/10.1016/j.ijsolstr.2011.08.012	journal	December 2011
Multi-scale defect interactions in high-rate failure of brittle materials, Part II: Application to design of protection materials Tonge, Andrew L.; Ramesh, K. T. Journal of the Mechanics and Physics of Solids, Vol. 86 https://doi.org/10.1016/j.jmps.2015.10.006	journal	January 2016
Material-point erosion simulation of dynamic fragmentation of metals Li, B.; Pandolfi, A.; Ortiz, M. Mechanics of Materials, Vol. 80 https://doi.org/10.1016/j.mechmat.2014.03.008	journal	January 2015
Effective Rheology Across the Fragmentation Transition for Sea Ice and Ice Shelves Åström, J. A.; Benn, D. I. Geophysical Research Letters, Vol. 46, Issue 22 https://doi.org/10.1029/2019GL084896	journal	November 2019
Nonlocal Damage Theory Pijaudier‐Cabot, Gilles; Bažant, Zdeněk P. Journal of Engineering Mechanics, Vol. 113, Issue 10 https://doi.org/10.1061/(ASCE)0733-9399(1987)113:10(1512)	journal	October 1987
Rate Dependent Damage Model for Concrete in Dynamics Dubé, Jean-François; Pijaudier-Cabot, Gilles; Borderie, Christian La Journal of Engineering Mechanics, Vol. 122, Issue 10 https://doi.org/10.1061/(ASCE)0733-9399(1996)122:10(939)	journal	October 1996
Instability, Ductility, and Size Effect in Strain-Softening Concrete Bažant, Zdeněk P. Journal of the Engineering Mechanics Division, Vol. 102, Issue 2 https://doi.org/10.1061/JMCEA3.0002111	journal	April 1976
Local inertial effects in dynamic fragmentation Grady, D. E. Journal of Applied Physics, Vol. 53, Issue 1, p. 322-325 https://doi.org/10.1063/1.329934	journal	January 1982
Strain‐energy effects on dynamic fragmentation Glenn, L. A.; Chudnovsky, A. Journal of Applied Physics, Vol. 59, Issue 4 https://doi.org/10.1063/1.336532	journal	February 1986
Phase-Field Model of Mode III Dynamic Fracture Karma, Alain; Kessler, David A.; Levine, Herbert Physical Review Letters, Vol. 87, Issue 4 https://doi.org/10.1103/PhysRevLett.87.045501	journal	July 2001
Cohesive Zone Models: A Critical Review of Traction-Separation Relationships Across Fracture Surfaces Park, Kyoungsoo; Paulino, Glaucio H. Applied Mechanics Reviews, Vol. 64, Issue 6 https://doi.org/10.1115/1.4023110	journal	November 2011
Comparison between thick level set (TLS) and cohesive zone models Parrilla Gómez, Andrés; Moës, Nicolas; Stolz, Claude Advanced Modeling and Simulation in Engineering Sciences, Vol. 2, Issue 1 https://doi.org/10.1186/s40323-015-0041-9	journal	July 2015
An Energy Based Failure Criterion for use with Peridynamic States Foster, John; Silling, Stewart A.; Chen, Weinong International Journal for Multiscale Computational Engineering, Vol. 9, Issue 6 https://doi.org/10.1615/IntJMultCompEng.2011002407	journal	January 2011
Simulating Fragmentation and Fluid-Induced Fracture in Disordered Media Using Random Finite-Element Meshes Bishop, Joseph E.; Martinez, Mario J.; Newell, Pania International Journal for Multiscale Computational Engineering, Vol. 14, Issue 4 https://doi.org/10.1615/IntJMultCompEng.2016016908	journal	January 2016
Lipschitz regularization for softening material models: the Lip-field approach Moës, Nicolas; Chevaugeon, Nicolas Comptes Rendus. Mécanique, Vol. 349, Issue 2 https://doi.org/10.5802/crmeca.91	journal	January 2021
Analysis of the delayed damage model for three one-dimensional loading scenarii Zghal, Jihed; Moës, Nicolas Comptes Rendus. Physique, Vol. 21, Issue 6 https://doi.org/10.5802/crphys.42	journal	January 2020

Similar Records

A cohesive zone treatment for the material point method involving problems of large deformation and damage

Journal Article · Sat Sep 27 00:00:00 EDT 2025 · Computer Methods in Applied Mechanics and Engineering · OSTI ID:3003988

An analytically enriched finite element method for cohesive crack modeling.

Conference · Thu Apr 01 00:00:00 EDT 2010 · OSTI ID:1011660

Unified cohesive zone model (UCZM) for fracturing and fragmenting solids

Journal Article · Mon Oct 28 00:00:00 EDT 2024 · Engineering Fracture Mechanics · OSTI ID:2475603

Related Subjects

36 MATERIALS SCIENCE
Damage
Dynamic
Fracture
Fragmentation
Lip-field
Lipschitz

Fragmentation analysis of a bar with the Lip-field approach

Citation Formats

References (62)

Similar Records

Related Subjects