Parallel three-dimensional simulations of quasi-static elastoplastic solids
Abstract
Hypo-elastoplasticity is a flexible framework for modeling the mechanics of many hard materials under small elastic deformation and large plastic deformation. Under typical loading rates, most laboratory tests of these materials happen in the quasi-static limit, but there are few existing numerical methods tailor-made for this physical regime. Here, we extend to three dimensions a recent projection method for simulating quasi-static hypo-elastoplastic materials. The method is based on a mathematical correspondence to the incompressible Navier–Stokes equations, where the projection method of Chorin (1968) is an established numerical technique. We develop and utilize a three-dimensional parallel geometric multigrid solver employed to solve a linear system for the quasi-static projection. Our method is tested through simulation of three-dimensional shear band nucleation and growth, a precursor to failure in many materials. As an example system, we employ a physical model of a bulk metallic glass based on the shear transformation zone theory, but the method can be applied to any elastoplasticity model. We consider several examples of three-dimensional shear banding, and examine shear band formation in physically realistic materials with heterogeneous initial conditions under both simple shear deformation and boundary conditions inspired by friction welding.
- Authors:
-
- Harvard Univ., Cambridge, MA (United States)
- Harvard Univ., Cambridge, MA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
- Publication Date:
- Research Org.:
- Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC)
- OSTI Identifier:
- 1580840
- Alternate Identifier(s):
- OSTI ID: 1809395
- Grant/Contract Number:
- AC02-05CH11231
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Computer Physics Communications
- Additional Journal Information:
- Journal Volume: 257; Journal ID: ISSN 0010-4655
- Publisher:
- Elsevier
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; fluid mechanics; Chorin-type projection method; plasticity; elastoplasticity
Citation Formats
Boffi, Nicholas M., and Rycroft, Chris H.. Parallel three-dimensional simulations of quasi-static elastoplastic solids. United States: N. p., 2020.
Web. doi:10.1016/j.cpc.2020.107254.
Boffi, Nicholas M., & Rycroft, Chris H.. Parallel three-dimensional simulations of quasi-static elastoplastic solids. United States. https://doi.org/10.1016/j.cpc.2020.107254
Boffi, Nicholas M., and Rycroft, Chris H.. Sun .
"Parallel three-dimensional simulations of quasi-static elastoplastic solids". United States. https://doi.org/10.1016/j.cpc.2020.107254. https://www.osti.gov/servlets/purl/1580840.
@article{osti_1580840,
title = {Parallel three-dimensional simulations of quasi-static elastoplastic solids},
author = {Boffi, Nicholas M. and Rycroft, Chris H.},
abstractNote = {Hypo-elastoplasticity is a flexible framework for modeling the mechanics of many hard materials under small elastic deformation and large plastic deformation. Under typical loading rates, most laboratory tests of these materials happen in the quasi-static limit, but there are few existing numerical methods tailor-made for this physical regime. Here, we extend to three dimensions a recent projection method for simulating quasi-static hypo-elastoplastic materials. The method is based on a mathematical correspondence to the incompressible Navier–Stokes equations, where the projection method of Chorin (1968) is an established numerical technique. We develop and utilize a three-dimensional parallel geometric multigrid solver employed to solve a linear system for the quasi-static projection. Our method is tested through simulation of three-dimensional shear band nucleation and growth, a precursor to failure in many materials. As an example system, we employ a physical model of a bulk metallic glass based on the shear transformation zone theory, but the method can be applied to any elastoplasticity model. We consider several examples of three-dimensional shear banding, and examine shear band formation in physically realistic materials with heterogeneous initial conditions under both simple shear deformation and boundary conditions inspired by friction welding.},
doi = {10.1016/j.cpc.2020.107254},
journal = {Computer Physics Communications},
number = ,
volume = 257,
place = {United States},
year = {2020},
month = {3}
}
Works referenced in this record:
A general theory of uniqueness and stability in elastic-plastic solids
journal, May 1958
- Hill, R.
- Journal of the Mechanics and Physics of Solids, Vol. 6, Issue 3
Bulk Metallic Glasses as Structural Materials: A Review: Bulk Metallic Glasses as Structural Materials: A Review
journal, May 2016
- Kruzic, Jamie J.
- Advanced Engineering Materials, Vol. 18, Issue 8
Fracture Toughness of Metallic Glasses: Annealing-Induced Embrittlement
journal, November 2012
- Rycroft, Chris H.; Bouchbinder, Eran
- Physical Review Letters, Vol. 109, Issue 19
Shear-transformation-zone theory of linear glassy dynamics
journal, June 2011
- Bouchbinder, Eran; Langer, J. S.
- Physical Review E, Vol. 83, Issue 6
Nonequilibrium thermodynamics of driven amorphous materials. I. Internal degrees of freedom and volume deformation
journal, September 2009
- Bouchbinder, Eran; Langer, J. S.
- Physical Review E, Vol. 80, Issue 3
Serrated flow and stick–slip deformation dynamics in the presence of shear-band interactions for a Zr-based metallic glass
journal, June 2012
- Sun, B. A.; Pauly, S.; Tan, J.
- Acta Materialia, Vol. 60, Issue 10
Shear band formation in plane strain
journal, January 1981
- Hutchinson, J. W.; Tvergaard, V.
- International Journal of Solids and Structures, Vol. 17, Issue 5
On the Partial Difference Equations of Mathematical Physics
journal, March 1967
- Courant, R.; Friedrichs, K.; Lewy, H.
- IBM Journal of Research and Development, Vol. 11, Issue 2
An adaptive displacement/pressure finite element scheme for treating incompressibility effects in elasto-plastic materials
journal, January 2001
- Suttmeier, Franz-Theo
- Numerical Methods for Partial Differential Equations, Vol. 17, Issue 4
Efficient implementation of essentially non-oscillatory shock-capturing schemes
journal, August 1988
- Shu, Chi-Wang; Osher, Stanley
- Journal of Computational Physics, Vol. 77, Issue 2
Thermodynamics of rate-independent plasticity
journal, March 2005
- Puglisi, G.; Truskinovsky, L.
- Journal of the Mechanics and Physics of Solids, Vol. 53, Issue 3
Shear-transformation-zone theory of plastic deformation near the glass transition
journal, February 2008
- Langer, J. S.
- Physical Review E, Vol. 77, Issue 2
A second-order projection method for the incompressible navier-stokes equations
journal, December 1989
- Bell, John B.; Colella, Phillip; Glaz, Harland M.
- Journal of Computational Physics, Vol. 85, Issue 2
Simulations of a stretching bar using a plasticity model from the shear transformation zone theory
journal, March 2012
- Rycroft, Chris H.; Gibou, Frédéric
- Journal of Computational Physics, Vol. 231, Issue 5
Numerical solution of the Navier-Stokes equations
journal, January 1968
- Chorin, Alexandre Joel
- Mathematics of Computation, Vol. 22, Issue 104
Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids
journal, July 1981
- Klainerman, Sergiu; Majda, Andrew
- Communications on Pure and Applied Mathematics, Vol. 34, Issue 4
Tensile ductility and necking of metallic glass
journal, August 2007
- Guo, H.; Yan, P. F.; Wang, Y. B.
- Nature Materials, Vol. 6, Issue 10
Adaptive low Mach number simulations of nuclear flame microphysics
journal, April 2004
- Bell, J. B.; Day, M. S.; Rendleman, C. A.
- Journal of Computational Physics, Vol. 195, Issue 2
Mechanical behavior of amorphous alloys
journal, July 2007
- Schuh, C.; Hufnagel, T.; Ramamurty, U.
- Acta Materialia, Vol. 55, Issue 12
On the analysis of rotation and stress rate in deforming bodies
journal, December 1979
- Dienes, J. K.
- Acta Mechanica, Vol. 32, Issue 4
A second order accurate projection method for the incompressible Navier–Stokes equations on non-graded adaptive grids
journal, December 2006
- Min, Chohong; Gibou, Frédéric
- Journal of Computational Physics, Vol. 219, Issue 2
Bulk Metallic Glasses Deform via Slip Avalanches
journal, April 2014
- Antonaglia, James; Wright, Wendelin J.; Gu, Xiaojun
- Physical Review Letters, Vol. 112, Issue 15
Microstructural evolution and mechanical properties of dissimilar Al–Cu joints produced by friction stir welding
journal, October 2013
- Tan, C. W.; Jiang, Z. G.; Li, L. Q.
- Materials & Design, Vol. 51
An Impulse-Based Approximation of Fluid Motion due to Boundary Forces
journal, February 1996
- Cortez, Ricardo
- Journal of Computational Physics, Vol. 123, Issue 2
Dynamics of viscoplastic deformation in amorphous solids
journal, June 1998
- Falk, M. L.; Langer, J. S.
- Physical Review E, Vol. 57, Issue 6
Dynamic evolution of nanoscale shear bands in a bulk-metallic glass
journal, April 2005
- Yang, Bing; Morrison, Mark L.; Liaw, Peter K.
- Applied Physics Letters, Vol. 86, Issue 14
Low Mach Number Modeling of Type Ia Supernovae. I. Hydrodynamics
journal, February 2006
- Almgren, A. S.; Bell, J. B.; Rendleman, C. A.
- The Astrophysical Journal, Vol. 637, Issue 2
Deformation and Failure of Amorphous, Solidlike Materials
journal, March 2011
- Falk, Michael L.; Langer, J. S.
- Annual Review of Condensed Matter Physics, Vol. 2, Issue 1
Finite rotation effects in numerical integration of rate constitutive equations arising in large-deformation analysis
journal, December 1980
- Hughes, Thomas J. R.; Winget, James
- International Journal for Numerical Methods in Engineering, Vol. 15, Issue 12
Notch Fracture Toughness of Glasses: Dependence on Rate, Age, and Geometry
journal, August 2016
- Vasoya, Manish; Rycroft, Chris H.; Bouchbinder, Eran
- Physical Review Applied, Vol. 6, Issue 2
Characterization of nanometer-scale defects in metallic glasses by quantitative high-resolution transmission electron microscopy
journal, March 2002
- Li, Jing; Wang, Z. L.; Hufnagel, T. C.
- Physical Review B, Vol. 65, Issue 14
Bifurcation analysis of the onset of necking in an elastic/plastic cylinder under uniaxial tension
journal, January 1974
- Hutchinson, J. W.; Miles, J. P.
- Journal of the Mechanics and Physics of Solids, Vol. 22, Issue 1
A single shear band in a metallic glass: Local core and wide soft zone
journal, October 2014
- Maaß, R.; Samwer, K.; Arnold, W.
- Applied Physics Letters, Vol. 105, Issue 17
An elementary discussion of definitions of stress rate
journal, January 1961
- Prager, William
- Quarterly of Applied Mathematics, Vol. 18, Issue 4
Finite element analysis of surface instability in hypo-elastic solids
journal, February 1990
- Bardet, J. P.
- Computer Methods in Applied Mechanics and Engineering, Vol. 78, Issue 3
Athermal shear-transformation-zone theory of amorphous plastic deformation. I. Basic principles
journal, March 2007
- Bouchbinder, Eran; Langer, J. S.; Procaccia, Itamar
- Physical Review E, Vol. 75, Issue 3
An Eulerian projection method for quasi-static elastoplasticity
journal, November 2015
- Rycroft, Chris H.; Sui, Yi; Bouchbinder, Eran
- Journal of Computational Physics, Vol. 300
A numerical method for solving incompressible viscous flow problems
journal, August 1967
- Chorin, Alexandre Joel
- Journal of Computational Physics, Vol. 2, Issue 1
Athermal shear-transformation-zone theory of amorphous plastic deformation. II. Analysis of simulated amorphous silicon
journal, March 2007
- Bouchbinder, Eran; Langer, J. S.; Procaccia, Itamar
- Physical Review E, Vol. 75, Issue 3
Mechanical glass transition revealed by the fracture toughness of metallic glasses
journal, August 2018
- Ketkaew, Jittisa; Chen, Wen; Wang, Hui
- Nature Communications, Vol. 9, Issue 1
A new hybrid numerical scheme for modelling elastodynamics in unbounded media with near-source heterogeneities
journal, August 2017
- Hajarolasvadi, Setare; Elbanna, Ahmed E.
- Geophysical Journal International, Vol. 211, Issue 2
Numerical vorticity creation based on impulse conservation.
journal, March 1996
- Summers, D. M.; Chorin, A. J.
- Proceedings of the National Academy of Sciences, Vol. 93, Issue 5
Softening Caused by Profuse Shear Banding in a Bulk Metallic Glass
journal, March 2006
- Bei, H.; Xie, S.; George, E. P.
- Physical Review Letters, Vol. 96, Issue 10
Coarse graining atomistic simulations of plastically deforming amorphous solids
journal, May 2017
- Hinkle, Adam R.; Rycroft, Chris H.; Shields, Michael D.
- Physical Review E, Vol. 95, Issue 5
Objective modeling of strain localization
journal, January 2002
- Jirásek, Milan
- Revue Française de Génie Civil, Vol. 6, Issue 6
A Multigrid Method on Non-Graded Adaptive Octree and Quadtree Cartesian Grids
journal, June 2012
- Theillard, Maxime; Rycroft, Chris H.; Gibou, Frédéric
- Journal of Scientific Computing, Vol. 55, Issue 1
Dynamics of Large-Scale Plastic Deformation and the Necking Instability in Amorphous Solids
journal, January 2003
- Eastgate, L. O.; Langer, J. S.; Pechenik, L.
- Physical Review Letters, Vol. 90, Issue 4
Accurate Projection Methods for the Incompressible Navier–Stokes Equations
journal, April 2001
- Brown, David L.; Cortez, Ricardo; Minion, Michael L.
- Journal of Computational Physics, Vol. 168, Issue 2
Elastoplasticity beyond small deformations
journal, March 2006
- Xiao, H.; Bruhns, O. T.; Meyers, A.
- Acta Mechanica, Vol. 182, Issue 1-2
Strain localization in dry sheared granular materials: A compactivity-based approach
journal, August 2018
- Ma, Xiao; Elbanna, Ahmed
- Physical Review E, Vol. 98, Issue 2
Shear band spacing under bending of Zr-based metallic glass plates
journal, May 2004
- Conner, R. D.; Li, Yi; Nix, W. D.
- Acta Materialia, Vol. 52, Issue 8
Some computational aspects of elastic-plastic large strain analysis
journal, January 1981
- Nagtegaal, J. C.; De Jong, J. E.
- International Journal for Numerical Methods in Engineering, Vol. 17, Issue 1
Implicit mesh discontinuous Galerkin methods and interfacial gauge methods for high-order accurate interface dynamics, with applications to surface tension dynamics, rigid body fluid–structure interaction, and free surface flow: Part II
journal, September 2017
- Saye, Robert
- Journal of Computational Physics, Vol. 344
Linear and rotary friction welding review
journal, February 2016
- Li, Wenya; Vairis, Achilles; Preuss, Michael
- International Materials Reviews, Vol. 61, Issue 2
Tensile instability and necking in materials with strain hardening and strain-rate hardening
journal, December 1977
- Ghosh, A. K.
- Acta Metallurgica, Vol. 25, Issue 12
Shear band formation in plane strain compression
journal, September 1988
- Harren, S. V.; Dève, H. E.; Asaro, R. J.
- Acta Metallurgica, Vol. 36, Issue 9
Effective temperature dynamics in an athermal amorphous plasticity theory
journal, May 2008
- Bouchbinder, Eran
- Physical Review E, Vol. 77, Issue 5
A hyperelastic-based large strain elasto-plastic constitutive formulation with combined isotropic-kinematic hardening using the logarithmic stress and strain measures
journal, October 1990
- Eterovic, Adrian Luis; Bathe, Klaus-Jürgen
- International Journal for Numerical Methods in Engineering, Vol. 30, Issue 6
Hypo-Elasticity
journal, January 1955
- Truesdell, C.
- Indiana University Mathematics Journal, Vol. 4, Issue 1
Implicit mesh discontinuous Galerkin methods and interfacial gauge methods for high-order accurate interface dynamics, with applications to surface tension dynamics, rigid body fluid–structure interaction, and free surface flow: Part I
journal, September 2017
- Saye, Robert
- Journal of Computational Physics, Vol. 344
Conditions for the localization of deformation in pressure-sensitive dilatant materials
journal, December 1975
- Rudnicki, J. W.; Rice, J. R.
- Journal of the Mechanics and Physics of Solids, Vol. 23, Issue 6
Shear-Band Dynamics in Metallic Glasses
journal, March 2015
- Maaß, Robert; Löffler, Jörg F.
- Advanced Functional Materials, Vol. 25, Issue 16
Iterative Methods by Space Decomposition and Subspace Correction
journal, December 1992
- Xu, Jinchao
- SIAM Review, Vol. 34, Issue 4
A Numerical Method for the Incompressible Navier-Stokes Equations Based on an Approximate Projection
journal, March 1996
- Almgren, Ann S.; Bell, John B.; Szymczak, William G.
- SIAM Journal on Scientific Computing, Vol. 17, Issue 2
An Adaptive Level Set Approach for Incompressible Two-Phase Flows
journal, January 1999
- Sussman, Mark; Almgren, Ann S.; Bell, John B.
- Journal of Computational Physics, Vol. 148, Issue 1
Shear bands in metallic glasses
journal, April 2013
- Greer, A. L.; Cheng, Y. Q.; Ma, E.
- Materials Science and Engineering: R: Reports, Vol. 74, Issue 4
Strain localization in ductile single crystals
journal, October 1977
- Asaro, R. J.; Rice, J. R.
- Journal of the Mechanics and Physics of Solids, Vol. 25, Issue 5
Thickness of shear bands in metallic glasses
journal, August 2006
- Zhang, Y.; Greer, A. L.
- Applied Physics Letters, Vol. 89, Issue 7
Strain localization in amorphous metals
journal, February 1982
- Steif, P. S.; Spaepen, F.; Hutchinson, J. W.
- Acta Metallurgica, Vol. 30, Issue 2
A computational procedure for rate-independent crystal plasticity
journal, April 1996
- Anand, L.; Kothari, M.
- Journal of the Mechanics and Physics of Solids, Vol. 44, Issue 4
Two-temperature continuum thermomechanics of deforming amorphous solids
journal, December 2014
- Kamrin, Ken; Bouchbinder, Eran
- Journal of the Mechanics and Physics of Solids, Vol. 73
Kinematic description of crystal plasticity in the finite kinematic framework: A micromechanical understanding of F=FeFp
journal, July 2014
- Reina, C.; Conti, S.
- Journal of the Mechanics and Physics of Solids, Vol. 67
Rate-dependent shear bands in a shear-transformation-zone model of amorphous solids
journal, January 2009
- Manning, M. L.; Daub, E. G.; Langer, J. S.
- Physical Review E, Vol. 79, Issue 1
Interfacial gauge methods for incompressible fluid dynamics
journal, June 2016
- Saye, Robert
- Science Advances, Vol. 2, Issue 6
Strain localization in a shear transformation zone model for amorphous solids
journal, November 2007
- Manning, M. L.; Langer, J. S.; Carlson, J. M.
- Physical Review E, Vol. 76, Issue 5
Necking instabilities in elastoviscoplastic materials
journal, July 2018
- Moriel, Avraham; Bouchbinder, Eran
- Physical Review Materials, Vol. 2, Issue 7
The Derivation and Numerical Solution of the Equations for Zero Mach Number Combustion
journal, January 1985
- Majda, Andfrew; Sethian, James
- Combustion Science and Technology, Vol. 42, Issue 3-4
Origin of Intermittent Plastic Flow and Instability of Shear Band Sliding in Bulk Metallic Glasses
journal, May 2013
- Sun, B. A.; Pauly, S.; Hu, J.
- Physical Review Letters, Vol. 110, Issue 22
Compressible and incompressible fluids
journal, September 1982
- Klainerman, Sergiu; Majda, Andrew
- Communications on Pure and Applied Mathematics, Vol. 35, Issue 5
Consistent tangent operators for rate-independent elastoplasticity
journal, February 1985
- Simo, J. C.; Taylor, R. L.
- Computer Methods in Applied Mechanics and Engineering, Vol. 48, Issue 1
Plastic deformation in metallic glasses
journal, January 1979
- Argon, A. S.
- Acta Metallurgica, Vol. 27, Issue 1
Necking in tensile bars with rectangular cross-section
journal, March 1993
- Tvergaard, Viggo
- Computer Methods in Applied Mechanics and Engineering, Vol. 103, Issue 1-2
Deformation and Failure of Zr 57 Ti 5 Cu 20 Ni 8 Al 10 Bulk Metallic Glass Under Quasi-static and Dynamic Compression
journal, June 2002
- Hufnagel, T. C.; Jiao, T.; Li, Y.
- Journal of Materials Research, Vol. 17, Issue 6
The effective temperature
journal, November 2011
- Cugliandolo, Leticia F.
- Journal of Physics A: Mathematical and Theoretical, Vol. 44, Issue 48
Tool geometry effect on the characteristics of dissimilar friction stir spot welded bulk metallic glass to lightweight alloys
journal, February 2014
- Shin, Hyung-Seop
- Journal of Alloys and Compounds, Vol. 586
Dynamical theory of shear bands in structural glasses
journal, January 2017
- Wisitsorasak, Apiwat; Wolynes, Peter G.
- Proceedings of the National Academy of Sciences, Vol. 114, Issue 6
Bulk Metallic Glasses as Structural Materials: A Review: Bulk Metallic Glasses as Structural Materials: A Review
journal, May 2016
- Kruzic, Jamie J.
- Advanced Engineering Materials, Vol. 18, Issue 8
Elastoplasticity beyond small deformations
journal, March 2006
- Xiao, H.; Bruhns, O. T.; Meyers, A.
- Acta Mechanica, Vol. 182, Issue 1-2
Shear band formation in plane strain compression
journal, September 1988
- Harren, S. V.; Dève, H. E.; Asaro, R. J.
- Acta Metallurgica, Vol. 36, Issue 9
Conditions for the localization of deformation in pressure-sensitive dilatant materials
journal, December 1975
- Rudnicki, J. W.; Rice, J. R.
- Journal of the Mechanics and Physics of Solids, Vol. 23, Issue 6
Finite element analysis of surface instability in hypo-elastic solids
journal, February 1990
- Bardet, J. P.
- Computer Methods in Applied Mechanics and Engineering, Vol. 78, Issue 3
Necking in tensile bars with rectangular cross-section
journal, March 1993
- Tvergaard, Viggo
- Computer Methods in Applied Mechanics and Engineering, Vol. 103, Issue 1-2
Thermodynamics of rate-independent plasticity
journal, March 2005
- Puglisi, G.; Truskinovsky, L.
- Journal of the Mechanics and Physics of Solids, Vol. 53, Issue 3
Two-dimensional contact analysis of elastic graded materials
journal, August 2000
- Giannakopoulos, A.
- Journal of the Mechanics and Physics of Solids, Vol. 48, Issue 8
Mechanical glass transition revealed by the fracture toughness of metallic glasses
journal, August 2018
- Ketkaew, Jittisa; Chen, Wen; Wang, Hui
- Nature Communications, Vol. 9, Issue 1
Dynamical theory of shear bands in structural glasses
journal, January 2017
- Wisitsorasak, Apiwat; Wolynes, Peter G.
- Proceedings of the National Academy of Sciences, Vol. 114, Issue 6
The Derivation and Numerical Solution of the Equations for Zero Mach Number Combustion
journal, January 1985
- Majda, Andfrew; Sethian, James
- Combustion Science and Technology, Vol. 42, Issue 3-4
Objective modeling of strain localization
journal, January 2002
- Jirásek, Milan
- Revue Française de Génie Civil, Vol. 6, Issue 6
Shear-Transformation-Zone Theory of Linear Glassy Dynamics
text, January 2011
- Bouchbinder, Eran; Langer, J. S.
- arXiv
Lubricated Immersed Boundary Method in Two Dimensions
text, January 2017
- Fai, Thomas G.; Rycroft, Chris H.
- arXiv