Coordinate transformation methodology for simulating quasistatic elastoplastic solids

Boffi, Nicholas M.; Rycroft, Chris H.

doi:10.1103/physreve.101.053304

Title: Coordinate transformation methodology for simulating quasistatic elastoplastic solids

Abstract

Molecular dynamics simulations frequently employ periodic boundary conditions where the positions of the periodic images are manipulated in order to apply deformation to the material sample. For example, Lees-Edwards conditions use moving periodic images to apply simple shear. Here, we examine the problem of precisely comparing this type of simulation to continuum solid mechanics. We employ a hypo-elastoplastic mechanical model, and develop a projection method to enforce quasi-static equilibrium. We introduce a simulation framework that uses a fixed Cartesian computational grid on a reference domain, and imposes deformation via a time-dependent coordinate transformation to the physical domain. As a test case for our method, we consider the evolution of shear bands in a bulk metallic glass using the shear transformation zone theory of amorphous plasticity. We examine the growth of shear bands in simple shear and pure shear conditions as a function of the initial preparation of the bulk metallic glass.

Authors:

Boffi, Nicholas M. ^[1];

^[2]

Harvard Univ., Cambridge, MA (United States). John A. Paulson School of Engineering and Applied Sciences (SEAS)
Harvard Univ., Cambridge, MA (United States). John A. Paulson School of Engineering and Applied Sciences (SEAS); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Computational Research Div.

Publication Date:: Fri May 08 00:00:00 EDT 2020

Research Org.:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

OSTI Identifier:: 1580841

Grant/Contract Number:: AC02-05CH11231; DMR-1409560; DMS-1753203

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review. E

Additional Journal Information:: Journal Volume: 101; Journal Issue: 5; Journal ID: ISSN 2470-0045

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 74 ATOMIC AND MOLECULAR PHYSICS; 97 MATHEMATICS AND COMPUTING; fluid mechanics; projection method; plasticity; elastoplasticity

Citation Formats


                    Boffi, Nicholas M., and Rycroft, Chris H. Coordinate transformation methodology for simulating quasistatic elastoplastic solids.  United States: N. p., 2020. 
Web.  doi:10.1103/physreve.101.053304.

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                    Boffi, Nicholas M., & Rycroft, Chris H. Coordinate transformation methodology for simulating quasistatic elastoplastic solids.  United States.  https://doi.org/10.1103/physreve.101.053304

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                    Boffi, Nicholas M., and Rycroft, Chris H. Fri .  
"Coordinate transformation methodology for simulating quasistatic elastoplastic solids".  United States.  https://doi.org/10.1103/physreve.101.053304.  https://www.osti.gov/servlets/purl/1580841.

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@article{osti_1580841,

  title        = {Coordinate transformation methodology for simulating quasistatic elastoplastic solids},

  author       = {Boffi, Nicholas M. and Rycroft, Chris H.},

  abstractNote = {Molecular dynamics simulations frequently employ periodic boundary conditions where the positions of the periodic images are manipulated in order to apply deformation to the material sample. For example, Lees-Edwards conditions use moving periodic images to apply simple shear. Here, we examine the problem of precisely comparing this type of simulation to continuum solid mechanics. We employ a hypo-elastoplastic mechanical model, and develop a projection method to enforce quasi-static equilibrium. We introduce a simulation framework that uses a fixed Cartesian computational grid on a reference domain, and imposes deformation via a time-dependent coordinate transformation to the physical domain. As a test case for our method, we consider the evolution of shear bands in a bulk metallic glass using the shear transformation zone theory of amorphous plasticity. We examine the growth of shear bands in simple shear and pure shear conditions as a function of the initial preparation of the bulk metallic glass.},

  doi          = {10.1103/physreve.101.053304},

  journal      = {Physical Review. E},

  number       = 5,

  volume       = 101,

  place        = {United States},

  year         = {Fri May 08 00:00:00 EDT 2020},

  month        = {Fri May 08 00:00:00 EDT 2020}

}

Copy to clipboard

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Works referenced in this record:

Amorphous systems in athermal, quasistatic shear
journal, July 2006

Maloney, Craig E.; Lemaître, Anaël
Physical Review E, Vol. 74, Issue 1
DOI: 10.1103/PhysRevE.74.016118

Many-body interactions and correlations in coarse-grained descriptions of polymer solutions
journal, July 2001

Bolhuis, P. G.; Louis, A. A.; Hansen, J. P.
Physical Review E, Vol. 64, Issue 2
DOI: 10.1103/PhysRevE.64.021801

A Multigrid Tutorial, Second Edition
book, January 2000

Briggs, William L.; Henson, Van Emden; McCormick, Steve F.
Other Titles in Applied Mathematics
DOI: 10.1137/1.9780898719505

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
DOI: 10.1016/0022-5096(58)90029-2

Thermodynamic theory of dislocation-mediated plasticity
journal, June 2010

Langer, J. S.; Bouchbinder, Eran; Lookman, Turab
Acta Materialia, Vol. 58, Issue 10
DOI: 10.1016/j.actamat.2010.03.009

Fracture Toughness of Metallic Glasses: Annealing-Induced Embrittlement
journal, November 2012

Rycroft, Chris H.; Bouchbinder, Eran
Physical Review Letters, Vol. 109, Issue 19
DOI: 10.1103/PhysRevLett.109.194301

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
DOI: 10.1103/PhysRevE.80.031131

Fracture behaviors under pure shear loading in bulk metallic glasses
journal, December 2016

Chen, Cen; Gao, Meng; Wang, Chao
Scientific Reports, Vol. 6, Issue 1
DOI: 10.1038/srep39522

Nonequilibrium thermodynamics of driven amorphous materials. III. Shear-transformation-zone plasticity
journal, September 2009

Bouchbinder, Eran; Langer, J. S.
Physical Review E, Vol. 80, Issue 3
DOI: 10.1103/PhysRevE.80.031133

Level Set Methods and Dynamic Implicit Surfaces
book, January 2003

Osher, Stanley; Fedkiw, Ronald
Applied Mathematical Sciences
DOI: 10.1007/b98879

Nonequilibrium thermodynamics of driven amorphous materials. II. Effective-temperature theory
journal, September 2009

Bouchbinder, Eran; Langer, J. S.
Physical Review E, Vol. 80, Issue 3
DOI: 10.1103/PhysRevE.80.031132

Phase diagram of highly asymmetric binary hard-sphere mixtures
journal, May 1999

Dijkstra, Marjolein; van Roij, René; Evans, Robert
Physical Review E, Vol. 59, Issue 5
DOI: 10.1103/PhysRevE.59.5744

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
DOI: 10.1147/rd.112.0215

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
DOI: 10.1016/0021-9991(88)90177-5

Time-dependent elastic response to a local shear transformation in amorphous solids
journal, April 2014

Puosi, F.; Rottler, J.; Barrat, J-L.
Physical Review E, Vol. 89, Issue 4
DOI: 10.1103/PhysRevE.89.042302

Molecular-dynamics study of ductile and brittle fracture in model noncrystalline solids
journal, September 1999

Falk, M. L.
Physical Review B, Vol. 60, Issue 10
DOI: 10.1103/PhysRevB.60.7062

Shear-transformation-zone theory of plastic deformation near the glass transition
journal, February 2008

Langer, J. S.
Physical Review E, Vol. 77, Issue 2
DOI: 10.1103/PhysRevE.77.021502

Fast Parallel Algorithms for Short-Range Molecular Dynamics
journal, March 1995

Plimpton, Steve
Journal of Computational Physics, Vol. 117, Issue 1
DOI: 10.1006/jcph.1995.1039

Subextensive Scaling in the Athermal, Quasistatic Limit of Amorphous Matter in Plastic Shear Flow
journal, July 2004

Maloney, Craig; Lemaître, Anaël
Physical Review Letters, Vol. 93, Issue 1
DOI: 10.1103/PhysRevLett.93.016001

A new algorithm for unrestricted duration nonequilibrium molecular dynamics simulations of planar elongational flow
journal, March 1999

Todd, B. D.; Daivis, Peter J.
Computer Physics Communications, Vol. 117, Issue 3
DOI: 10.1016/S0010-4655(98)00178-7

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
DOI: 10.1016/j.jcp.2011.10.009

A micromechanics-based nonlocal constitutive equation and estimates of representative volume element size for elastic composites
journal, April 1996

Drugan, W. J.; Willis, J. R.
Journal of the Mechanics and Physics of Solids, Vol. 44, Issue 4
DOI: 10.1016/0022-5096(96)00007-5

Periodic boundary conditions for long-time nonequilibrium molecular dynamics simulations of incompressible flows
journal, November 2014

Dobson, Matthew
The Journal of Chemical Physics, Vol. 141, Issue 18
DOI: 10.1063/1.4901276

Numerical solution of the Navier-Stokes equations
journal, January 1968

Chorin, Alexandre Joel
Mathematics of Computation, Vol. 22, Issue 104
DOI: 10.1090/S0025-5718-1968-0242392-2

Strain Localization and Percolation of Stable Structure in Amorphous Solids
journal, August 2005

Shi, Yunfeng; Falk, Michael L.
Physical Review Letters, Vol. 95, Issue 9
DOI: 10.1103/PhysRevLett.95.095502

Phase-Field Model of Mode III Dynamic Fracture
journal, July 2001

Karma, Alain; Kessler, David A.; Levine, Herbert
Physical Review Letters, Vol. 87, Issue 4
DOI: 10.1103/PhysRevLett.87.045501

Mechanical behavior of amorphous alloys
journal, July 2007

Schuh, C.; Hufnagel, T.; Ramamurty, U.
Acta Materialia, Vol. 55, Issue 12
DOI: 10.1016/j.actamat.2007.01.052

Experimental measurement of an effective temperature for jammed granular materials
journal, February 2005

Song, C.; Wang, P.; Makse, H. A.
Proceedings of the National Academy of Sciences, Vol. 102, Issue 7
DOI: 10.1073/pnas.0409911102

A Review of Material Frame-Indifference in Mechanics
journal, August 1998

Speziale, Charles G.
Applied Mechanics Reviews, Vol. 51, Issue 8
DOI: 10.1115/1.3099017

Atomistic simulations of Mg–Cu metallic glasses: mechanical properties
journal, December 2004

Bailey, Nicholas P.; Schiøtz, Jakob; Jacobsen, Karsten W.
Materials Science and Engineering: A, Vol. 387-389
DOI: 10.1016/j.msea.2003.11.092

Bulk Glass-Forming Metallic Alloys: Science and Technology
journal, October 1999

Johnson, William L.
MRS Bulletin, Vol. 24, Issue 10
DOI: 10.1557/S0883769400053252

Compaction of granular mixtures: a free volume model
journal, October 1997

Boutreux, T.; de Geennes, P. G.
Physica A: Statistical Mechanics and its Applications, Vol. 244, Issue 1-4
DOI: 10.1016/S0378-4371(97)00236-7

Dynamics of viscoplastic deformation in amorphous solids
journal, June 1998

Falk, M. L.; Langer, J. S.
Physical Review E, Vol. 57, Issue 6
DOI: 10.1103/PhysRevE.57.7192

Molecular dynamics simulations of deformation mechanisms of amorphous polyethylene
journal, November 2010

Hossain, D.; Tschopp, M. A.; Ward, D. K.
Polymer, Vol. 51, Issue 25
DOI: 10.1016/j.polymer.2010.10.009

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
DOI: 10.1063/1.1891302

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
DOI: 10.1146/annurev-conmatphys-062910-140452

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
DOI: 10.1103/PhysRevApplied.6.024008

Onset of plasticity and its relation to atomic structure in CuZr metallic glass nanowire: A molecular dynamics study
journal, January 2016

Sepúlveda-Macías, Matías; Amigo, Nicolás; Gutiérrez, Gonzalo
Journal of Alloys and Compounds, Vol. 655
DOI: 10.1016/j.jallcom.2015.09.149

Deformation and fracture toughness of a bulk amorphous Zr–Ti–Ni–Cu–Be alloy
journal, May 2000

Lowhaphandu, P.; Ludrosky, L. A.; Montgomery, S. L.
Intermetallics, Vol. 8, Issue 5-6
DOI: 10.1016/S0966-9795(99)00137-5

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
DOI: 10.1103/PhysRevE.75.036107

Nonequilibrium Molecular Dynamics Simulations of Planar Elongational Flow with Spatially and Temporally Periodic Boundary Conditions
journal, August 1998

Todd, B.; Daivis, Peter
Physical Review Letters, Vol. 81, Issue 5
DOI: 10.1103/PhysRevLett.81.1118

A numerical method for solving incompressible viscous flow problems
journal, August 1967

Chorin, Alexandre Joel
Journal of Computational Physics, Vol. 2, Issue 1
DOI: 10.1016/0021-9991(67)90037-X

An Eulerian projection method for quasi-static elastoplasticity
journal, November 2015

Rycroft, Chris H.; Sui, Yi; Bouchbinder, Eran
Journal of Computational Physics, Vol. 300
DOI: 10.1016/j.jcp.2015.06.046

Bulk Metallic Glasses
journal, February 2013

Schroers, Jan
Physics Today, Vol. 66, Issue 2
DOI: 10.1063/PT.3.1885

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
DOI: 10.1103/PhysRevE.75.036108

Steady state simulation of planar elongation flow by nonequilibrium molecular dynamics
journal, January 1999

Baranyai, András; Cummings, Peter T.
The Journal of Chemical Physics, Vol. 110, Issue 1
DOI: 10.1063/1.478082

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
DOI: 10.1038/s41467-018-05682-8

Applied Numerical Linear Algebra
book, January 1997

Demmel, James W.
Society for Industrial and Applied Mathematics
DOI: 10.1137/1.9781611971446

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
DOI: 10.1103/PhysRevE.95.053001

GROMACS: A message-passing parallel molecular dynamics implementation
journal, September 1995

Berendsen, H. J. C.; van der Spoel, D.; van Drunen, R.
Computer Physics Communications, Vol. 91, Issue 1-3
DOI: 10.1016/0010-4655(95)00042-E

Reversibility and criticality in amorphous solids
journal, November 2015

Regev, Ido; Weber, John; Reichhardt, Charles
Nature Communications, Vol. 6, Issue 1
DOI: 10.1038/ncomms9805

Deformation Mechanisms of the Zr₄₀Ti₁₄Ni₁₀Cu₁₂Be₂₄ Bulk Metallic Glass
journal, January 2001

Wright, Wendelin J.; Saha, Ranjana; Nix, William D.
MATERIALS TRANSACTIONS, Vol. 42, Issue 4
DOI: 10.2320/matertrans.42.642

Elastoplasticity beyond small deformations
journal, March 2006

Xiao, H.; Bruhns, O. T.; Meyers, A.
Acta Mechanica, Vol. 182, Issue 1-2
DOI: 10.1007/s00707-005-0282-7

Determination of the size of the representative volume element for random composites: statistical and numerical approach
journal, June 2003

Kanit, T.; Forest, S.; Galliet, I.
International Journal of Solids and Structures, Vol. 40, Issue 13-14
DOI: 10.1016/S0020-7683(03)00143-4

Pure shear stress reversal on a Cu-based bulk metallic glass reveals a Bauschinger-type effect
journal, December 2014

Sun, Yong Hao; Louzguine-Luzgin, D. V.; Ketov, S.
Journal of Alloys and Compounds, Vol. 615
DOI: 10.1016/j.jallcom.2013.11.104

On factors influencing the ductile-to-brittle transition in a bulk metallic glass
journal, June 2009

Raghavan, R.; Murali, P.; Ramamurty, U.
Acta Materialia, Vol. 57, Issue 11
DOI: 10.1016/j.actamat.2009.03.047

Effective temperature dynamics in an athermal amorphous plasticity theory
journal, May 2008

Bouchbinder, Eran
Physical Review E, Vol. 77, Issue 5
DOI: 10.1103/PhysRevE.77.051505

Difference in compressive and tensile fracture mechanisms of Zr59Cu20Al10Ni8Ti3 bulk metallic glass
journal, February 2003

Zhang, Z. F.; Eckert, J.; Schultz, L.
Acta Materialia, Vol. 51, Issue 4
DOI: 10.1016/S1359-6454(02)00521-9

Hypo-Elasticity
journal, January 1955

Truesdell, C.
Indiana University Mathematics Journal, Vol. 4, Issue 1
DOI: 10.1512/iumj.1955.4.54002

Fatigue and fracture behavior of bulk metallic glass
journal, November 2004

Zhang, Z. F.; Eckert, J.; Schultz, L.
Metallurgical and Materials Transactions A, Vol. 35, Issue 11
DOI: 10.1007/s11661-004-0186-5

Representative volume element size for elastic composites: A numerical study
journal, September 1997

Gusev, Andrei A.
Journal of the Mechanics and Physics of Solids, Vol. 45, Issue 9
DOI: 10.1016/S0022-5096(97)00016-1

Shear-Band Dynamics in Metallic Glasses
journal, March 2015

Maaß, Robert; Löffler, Jörg F.
Advanced Functional Materials, Vol. 25, Issue 16
DOI: 10.1002/adfm.201404223

Extensional motions of spatially periodic lattices
journal, November 1992

Kraynik, A. M.; Reinelt, D. A.
International Journal of Multiphase Flow, Vol. 18, Issue 6
DOI: 10.1016/0301-9322(92)90074-Q

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
DOI: 10.1016/j.mser.2013.04.001

A review of some plasticity and viscoplasticity constitutive theories
journal, October 2008

Chaboche, J. L.
International Journal of Plasticity, Vol. 24, Issue 10
DOI: 10.1016/j.ijplas.2008.03.009

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
DOI: 10.1016/j.jmps.2014.09.009

Steady-state, effective-temperature dynamics in a glassy material
journal, November 2007

Langer, J. S.; Manning, M. L.
Physical Review E, Vol. 76, Issue 5
DOI: 10.1103/PhysRevE.76.056107

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
DOI: 10.1103/PhysRevE.79.016110

The computer study of transport processes under extreme conditions
journal, August 1972

Lees, A. W.; Edwards, S. F.
Journal of Physics C: Solid State Physics, Vol. 5, Issue 15
DOI: 10.1088/0022-3719/5/15/006

Liquid-glass transition, a free-volume approach
journal, August 1979

Cohen, Morrel H.; Grest, G. S.
Physical Review B, Vol. 20, Issue 3
DOI: 10.1103/PhysRevB.20.1077

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
DOI: 10.1103/PhysRevE.76.056106

A microscopic mechanism for steady state inhomogeneous flow in metallic glasses
journal, April 1977

Spaepen, Frans
Acta Metallurgica, Vol. 25, Issue 4
DOI: 10.1016/0001-6160(77)90232-2

Parallel three-dimensional simulations of quasi-static elastoplastic solids
journal, March 2020

Boffi, Nicholas M.; Rycroft, Chris H.
Computer Physics Communications
DOI: 10.1016/j.cpc.2020.107254

Plastic deformation in metallic glasses
journal, January 1979

Argon, A. S.
Acta Metallurgica, Vol. 27, Issue 1
DOI: 10.1016/0001-6160(79)90055-5

Cavitation in Amorphous Solids
journal, April 2013

Guan, Pengfei; Lu, Shuo; Spector, Michael J. B.
Physical Review Letters, Vol. 110, Issue 18
DOI: 10.1103/PhysRevLett.110.185502

The effective temperature
journal, November 2011

Cugliandolo, Leticia F.
Journal of Physics A: Mathematical and Theoretical, Vol. 44, Issue 48
DOI: 10.1088/1751-8113/44/48/483001

Granular flow in pebble-bed nuclear reactors: Scaling, dust generation, and stress
journal, December 2013

Rycroft, Chris H.; Dehbi, Abdel; Lind, Terttaliisa
Nuclear Engineering and Design, Vol. 265
DOI: 10.1016/j.nucengdes.2013.07.010

Stability of an expanding circular cavity and the failure of amorphous solids
journal, August 2008

Bouchbinder, Eran; Lo, Ting-Shek; Procaccia, Itamar
Physical Review E, Vol. 78, Issue 2
DOI: 10.1103/PhysRevE.78.026124

Confined granular packings: Structure, stress, and forces
journal, April 2003

Landry, James W.; Grest, Gary S.; Silbert, Leonardo E.
Physical Review E, Vol. 67, Issue 4
DOI: 10.1103/PhysRevE.67.041303

A micromechanics-based nonlocal constitutive equation and estimates of representative volume element size for elastic composites
journal, April 1996

Drugan, W. J.; Willis, J. R.
Journal of the Mechanics and Physics of Solids, Vol. 44, Issue 4
DOI: 10.1016/0022-5096(96)00007-5

Nonequilibrium Thermodynamics of Amorphous Materials II: Effective-Temperature Theory
text, January 2009

Bouchbinder, Eran; Langer, J. S.
arXiv
DOI: 10.48550/arxiv.0903.1524

Time dependent elastic response to a local shear transformation in amorphous solids
text, January 2014

Puosi, Francesco; Rottler, Joerg; Barrat, Jean-Louis
arXiv
DOI: 10.48550/arxiv.1402.1474

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Fracture Toughness of Metallic Glasses: Annealing-Induced Embrittlement journal, November 2012

Nonequilibrium thermodynamics of driven amorphous materials. I. Internal degrees of freedom and volume deformation journal, September 2009

Fracture behaviors under pure shear loading in bulk metallic glasses journal, December 2016

Nonequilibrium thermodynamics of driven amorphous materials. III. Shear-transformation-zone plasticity journal, September 2009

Level Set Methods and Dynamic Implicit Surfaces book, January 2003

Nonequilibrium thermodynamics of driven amorphous materials. II. Effective-temperature theory journal, September 2009

Phase diagram of highly asymmetric binary hard-sphere mixtures journal, May 1999

On the Partial Difference Equations of Mathematical Physics journal, March 1967

Efficient implementation of essentially non-oscillatory shock-capturing schemes journal, August 1988

Time-dependent elastic response to a local shear transformation in amorphous solids journal, April 2014

Molecular-dynamics study of ductile and brittle fracture in model noncrystalline solids journal, September 1999

Shear-transformation-zone theory of plastic deformation near the glass transition journal, February 2008

Fast Parallel Algorithms for Short-Range Molecular Dynamics journal, March 1995

Subextensive Scaling in the Athermal, Quasistatic Limit of Amorphous Matter in Plastic Shear Flow journal, July 2004

A new algorithm for unrestricted duration nonequilibrium molecular dynamics simulations of planar elongational flow journal, March 1999

Simulations of a stretching bar using a plasticity model from the shear transformation zone theory journal, March 2012

A micromechanics-based nonlocal constitutive equation and estimates of representative volume element size for elastic composites journal, April 1996

Periodic boundary conditions for long-time nonequilibrium molecular dynamics simulations of incompressible flows journal, November 2014

Numerical solution of the Navier-Stokes equations journal, January 1968

Strain Localization and Percolation of Stable Structure in Amorphous Solids journal, August 2005

Phase-Field Model of Mode III Dynamic Fracture journal, July 2001

Mechanical behavior of amorphous alloys journal, July 2007

Experimental measurement of an effective temperature for jammed granular materials journal, February 2005

A Review of Material Frame-Indifference in Mechanics journal, August 1998

Atomistic simulations of Mg–Cu metallic glasses: mechanical properties journal, December 2004

Bulk Glass-Forming Metallic Alloys: Science and Technology journal, October 1999

Compaction of granular mixtures: a free volume model journal, October 1997

Dynamics of viscoplastic deformation in amorphous solids journal, June 1998

Molecular dynamics simulations of deformation mechanisms of amorphous polyethylene journal, November 2010

Dynamic evolution of nanoscale shear bands in a bulk-metallic glass journal, April 2005

Deformation and Failure of Amorphous, Solidlike Materials journal, March 2011

Notch Fracture Toughness of Glasses: Dependence on Rate, Age, and Geometry journal, August 2016

Onset of plasticity and its relation to atomic structure in CuZr metallic glass nanowire: A molecular dynamics study journal, January 2016

Deformation and fracture toughness of a bulk amorphous Zr–Ti–Ni–Cu–Be alloy journal, May 2000

Athermal shear-transformation-zone theory of amorphous plastic deformation. I. Basic principles journal, March 2007

Nonequilibrium Molecular Dynamics Simulations of Planar Elongational Flow with Spatially and Temporally Periodic Boundary Conditions journal, August 1998

A numerical method for solving incompressible viscous flow problems journal, August 1967

An Eulerian projection method for quasi-static elastoplasticity journal, November 2015

Bulk Metallic Glasses journal, February 2013

Athermal shear-transformation-zone theory of amorphous plastic deformation. II. Analysis of simulated amorphous silicon journal, March 2007

Steady state simulation of planar elongation flow by nonequilibrium molecular dynamics journal, January 1999

Mechanical glass transition revealed by the fracture toughness of metallic glasses journal, August 2018

Applied Numerical Linear Algebra book, January 1997

Coarse graining atomistic simulations of plastically deforming amorphous solids journal, May 2017

GROMACS: A message-passing parallel molecular dynamics implementation journal, September 1995

Reversibility and criticality in amorphous solids journal, November 2015

Deformation Mechanisms of the Zr40Ti14Ni10Cu12Be24 Bulk Metallic Glass journal, January 2001

Elastoplasticity beyond small deformations journal, March 2006

Determination of the size of the representative volume element for random composites: statistical and numerical approach journal, June 2003

Pure shear stress reversal on a Cu-based bulk metallic glass reveals a Bauschinger-type effect journal, December 2014

On factors influencing the ductile-to-brittle transition in a bulk metallic glass journal, June 2009

Effective temperature dynamics in an athermal amorphous plasticity theory journal, May 2008

Difference in compressive and tensile fracture mechanisms of Zr59Cu20Al10Ni8Ti3 bulk metallic glass journal, February 2003

Hypo-Elasticity journal, January 1955

Fatigue and fracture behavior of bulk metallic glass journal, November 2004

Representative volume element size for elastic composites: A numerical study journal, September 1997

Shear-Band Dynamics in Metallic Glasses journal, March 2015

Extensional motions of spatially periodic lattices journal, November 1992

Shear bands in metallic glasses journal, April 2013

A review of some plasticity and viscoplasticity constitutive theories journal, October 2008

Two-temperature continuum thermomechanics of deforming amorphous solids journal, December 2014

Steady-state, effective-temperature dynamics in a glassy material journal, November 2007

Rate-dependent shear bands in a shear-transformation-zone model of amorphous solids journal, January 2009

The computer study of transport processes under extreme conditions journal, August 1972

Liquid-glass transition, a free-volume approach journal, August 1979

Strain localization in a shear transformation zone model for amorphous solids journal, November 2007

A microscopic mechanism for steady state inhomogeneous flow in metallic glasses journal, April 1977

Parallel three-dimensional simulations of quasi-static elastoplastic solids journal, March 2020

Plastic deformation in metallic glasses journal, January 1979

Cavitation in Amorphous Solids journal, April 2013

The effective temperature journal, November 2011

Granular flow in pebble-bed nuclear reactors: Scaling, dust generation, and stress journal, December 2013

Amorphous systems in athermal, quasistatic shear
journal, July 2006

Many-body interactions and correlations in coarse-grained descriptions of polymer solutions
journal, July 2001

A Multigrid Tutorial, Second Edition
book, January 2000

A general theory of uniqueness and stability in elastic-plastic solids
journal, May 1958

Thermodynamic theory of dislocation-mediated plasticity
journal, June 2010

Fracture Toughness of Metallic Glasses: Annealing-Induced Embrittlement
journal, November 2012

Nonequilibrium thermodynamics of driven amorphous materials. I. Internal degrees of freedom and volume deformation
journal, September 2009

Fracture behaviors under pure shear loading in bulk metallic glasses
journal, December 2016

Nonequilibrium thermodynamics of driven amorphous materials. III. Shear-transformation-zone plasticity
journal, September 2009

Level Set Methods and Dynamic Implicit Surfaces
book, January 2003

Nonequilibrium thermodynamics of driven amorphous materials. II. Effective-temperature theory
journal, September 2009

Phase diagram of highly asymmetric binary hard-sphere mixtures
journal, May 1999

On the Partial Difference Equations of Mathematical Physics
journal, March 1967

Efficient implementation of essentially non-oscillatory shock-capturing schemes
journal, August 1988

Time-dependent elastic response to a local shear transformation in amorphous solids
journal, April 2014

Molecular-dynamics study of ductile and brittle fracture in model noncrystalline solids
journal, September 1999

Shear-transformation-zone theory of plastic deformation near the glass transition
journal, February 2008

Fast Parallel Algorithms for Short-Range Molecular Dynamics
journal, March 1995

Subextensive Scaling in the Athermal, Quasistatic Limit of Amorphous Matter in Plastic Shear Flow
journal, July 2004

A new algorithm for unrestricted duration nonequilibrium molecular dynamics simulations of planar elongational flow
journal, March 1999

Simulations of a stretching bar using a plasticity model from the shear transformation zone theory
journal, March 2012

A micromechanics-based nonlocal constitutive equation and estimates of representative volume element size for elastic composites
journal, April 1996

Periodic boundary conditions for long-time nonequilibrium molecular dynamics simulations of incompressible flows
journal, November 2014

Numerical solution of the Navier-Stokes equations
journal, January 1968

Strain Localization and Percolation of Stable Structure in Amorphous Solids
journal, August 2005

Phase-Field Model of Mode III Dynamic Fracture
journal, July 2001

Mechanical behavior of amorphous alloys
journal, July 2007

Experimental measurement of an effective temperature for jammed granular materials
journal, February 2005

A Review of Material Frame-Indifference in Mechanics
journal, August 1998

Atomistic simulations of Mg–Cu metallic glasses: mechanical properties
journal, December 2004

Bulk Glass-Forming Metallic Alloys: Science and Technology
journal, October 1999

Compaction of granular mixtures: a free volume model
journal, October 1997

Dynamics of viscoplastic deformation in amorphous solids
journal, June 1998

Molecular dynamics simulations of deformation mechanisms of amorphous polyethylene
journal, November 2010

Dynamic evolution of nanoscale shear bands in a bulk-metallic glass
journal, April 2005

Deformation and Failure of Amorphous, Solidlike Materials
journal, March 2011

Notch Fracture Toughness of Glasses: Dependence on Rate, Age, and Geometry
journal, August 2016

Onset of plasticity and its relation to atomic structure in CuZr metallic glass nanowire: A molecular dynamics study
journal, January 2016

Deformation and fracture toughness of a bulk amorphous Zr–Ti–Ni–Cu–Be alloy
journal, May 2000

Athermal shear-transformation-zone theory of amorphous plastic deformation. I. Basic principles
journal, March 2007

Nonequilibrium Molecular Dynamics Simulations of Planar Elongational Flow with Spatially and Temporally Periodic Boundary Conditions
journal, August 1998

A numerical method for solving incompressible viscous flow problems
journal, August 1967

An Eulerian projection method for quasi-static elastoplasticity
journal, November 2015

Bulk Metallic Glasses
journal, February 2013

Athermal shear-transformation-zone theory of amorphous plastic deformation. II. Analysis of simulated amorphous silicon
journal, March 2007

Steady state simulation of planar elongation flow by nonequilibrium molecular dynamics
journal, January 1999

Mechanical glass transition revealed by the fracture toughness of metallic glasses
journal, August 2018

Applied Numerical Linear Algebra
book, January 1997

Coarse graining atomistic simulations of plastically deforming amorphous solids
journal, May 2017

GROMACS: A message-passing parallel molecular dynamics implementation
journal, September 1995

Reversibility and criticality in amorphous solids
journal, November 2015

Deformation Mechanisms of the Zr₄₀Ti₁₄Ni₁₀Cu₁₂Be₂₄ Bulk Metallic Glass
journal, January 2001

Elastoplasticity beyond small deformations
journal, March 2006

Determination of the size of the representative volume element for random composites: statistical and numerical approach
journal, June 2003

Pure shear stress reversal on a Cu-based bulk metallic glass reveals a Bauschinger-type effect
journal, December 2014

On factors influencing the ductile-to-brittle transition in a bulk metallic glass
journal, June 2009

Effective temperature dynamics in an athermal amorphous plasticity theory
journal, May 2008

Difference in compressive and tensile fracture mechanisms of Zr59Cu20Al10Ni8Ti3 bulk metallic glass
journal, February 2003

Hypo-Elasticity
journal, January 1955

Fatigue and fracture behavior of bulk metallic glass
journal, November 2004

Representative volume element size for elastic composites: A numerical study
journal, September 1997

Shear-Band Dynamics in Metallic Glasses
journal, March 2015

Extensional motions of spatially periodic lattices
journal, November 1992

Shear bands in metallic glasses
journal, April 2013

A review of some plasticity and viscoplasticity constitutive theories
journal, October 2008

Two-temperature continuum thermomechanics of deforming amorphous solids
journal, December 2014

Steady-state, effective-temperature dynamics in a glassy material
journal, November 2007

Rate-dependent shear bands in a shear-transformation-zone model of amorphous solids
journal, January 2009

The computer study of transport processes under extreme conditions
journal, August 1972

Liquid-glass transition, a free-volume approach
journal, August 1979

Strain localization in a shear transformation zone model for amorphous solids
journal, November 2007

A microscopic mechanism for steady state inhomogeneous flow in metallic glasses
journal, April 1977

Parallel three-dimensional simulations of quasi-static elastoplastic solids
journal, March 2020

Plastic deformation in metallic glasses
journal, January 1979

Cavitation in Amorphous Solids
journal, April 2013

The effective temperature
journal, November 2011

Granular flow in pebble-bed nuclear reactors: Scaling, dust generation, and stress
journal, December 2013

Stability of an expanding circular cavity and the failure of amorphous solids
journal, August 2008

Confined granular packings: Structure, stress, and forces
journal, April 2003

A micromechanics-based nonlocal constitutive equation and estimates of representative volume element size for elastic composites
journal, April 1996