Parallel three-dimensional simulations of quasi-static elastoplastic solids

Boffi, Nicholas M.; Rycroft, Chris H.

doi:10.1016/j.cpc.2020.107254

Title: 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:

Boffi, Nicholas M. ^[1]; Rycroft, Chris H. ^[2]

Harvard Univ., Cambridge, MA (United States)
Harvard Univ., Cambridge, MA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

Publication Date:: Sun Mar 01 00:00:00 EST 2020

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.

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                    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

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                    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.

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@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         = {Sun Mar 01 00:00:00 EST 2020},

  month        = {Sun Mar 01 00:00:00 EST 2020}

}

Copy to clipboard

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Wisitsorasak, Apiwat; Wolynes, Peter G.
Proceedings of the National Academy of Sciences, Vol. 114, Issue 6
DOI: 10.1073/pnas.1620399114

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
DOI: 10.1080/00102208508960376

Objective modeling of strain localization
journal, January 2002

Jirásek, Milan
Revue Française de Génie Civil, Vol. 6, Issue 6
DOI: 10.1080/12795119.2002.9692735

Shear-Transformation-Zone Theory of Linear Glassy Dynamics
text, January 2011

Bouchbinder, Eran; Langer, J. S.
arXiv
DOI: 10.48550/arxiv.1101.2015

Lubricated Immersed Boundary Method in Two Dimensions
text, January 2017

Fai, Thomas G.; Rycroft, Chris H.
arXiv
DOI: 10.48550/arxiv.1701.08865

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Title: Parallel three-dimensional simulations of quasi-static elastoplastic solids

Abstract

Citation Formats

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

Bulk Metallic Glasses as Structural Materials: A Review: Bulk Metallic Glasses as Structural Materials: A Review journal, May 2016

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

Shear-transformation-zone theory of linear glassy dynamics journal, June 2011

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

Serrated flow and stick–slip deformation dynamics in the presence of shear-band interactions for a Zr-based metallic glass journal, June 2012

Shear band formation in plane strain journal, January 1981

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

An adaptive displacement/pressure finite element scheme for treating incompressibility effects in elasto-plastic materials journal, January 2001

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

Thermodynamics of rate-independent plasticity journal, March 2005

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

A second-order projection method for the incompressible navier-stokes equations journal, December 1989

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

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

Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids journal, July 1981

Tensile ductility and necking of metallic glass journal, August 2007

Adaptive low Mach number simulations of nuclear flame microphysics journal, April 2004

Mechanical behavior of amorphous alloys journal, July 2007

On the analysis of rotation and stress rate in deforming bodies journal, December 1979

A second order accurate projection method for the incompressible Navier–Stokes equations on non-graded adaptive grids journal, December 2006

Bulk Metallic Glasses Deform via Slip Avalanches journal, April 2014

Microstructural evolution and mechanical properties of dissimilar Al–Cu joints produced by friction stir welding journal, October 2013

An Impulse-Based Approximation of Fluid Motion due to Boundary Forces journal, February 1996

Dynamics of viscoplastic deformation in amorphous solids journal, June 1998

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

Low Mach Number Modeling of Type Ia Supernovae. I. Hydrodynamics journal, February 2006

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

Finite rotation effects in numerical integration of rate constitutive equations arising in large-deformation analysis journal, December 1980

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

Open MPI: Goals, Concept, and Design of a Next Generation MPI Implementation book, January 2004

Characterization of nanometer-scale defects in metallic glasses by quantitative high-resolution transmission electron microscopy journal, March 2002

Bifurcation analysis of the onset of necking in an elastic/plastic cylinder under uniaxial tension journal, January 1974

A single shear band in a metallic glass: Local core and wide soft zone journal, October 2014

An elementary discussion of definitions of stress rate journal, January 1961

Finite element analysis of surface instability in hypo-elastic solids journal, February 1990

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

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

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

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

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

A new hybrid numerical scheme for modelling elastodynamics in unbounded media with near-source heterogeneities journal, August 2017

Numerical vorticity creation based on impulse conservation. journal, March 1996

Softening Caused by Profuse Shear Banding in a Bulk Metallic Glass journal, March 2006

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

Objective modeling of strain localization journal, January 2002

A Multigrid Method on Non-Graded Adaptive Octree and Quadtree Cartesian Grids journal, June 2012

Dynamics of Large-Scale Plastic Deformation and the Necking Instability in Amorphous Solids journal, January 2003

Accurate Projection Methods for the Incompressible Navier–Stokes Equations journal, April 2001

Elastoplasticity beyond small deformations journal, March 2006

Strain localization in dry sheared granular materials: A compactivity-based approach journal, August 2018

Shear band spacing under bending of Zr-based metallic glass plates journal, May 2004

Some computational aspects of elastic-plastic large strain analysis journal, January 1981

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

Linear and rotary friction welding review journal, February 2016

Tensile instability and necking in materials with strain hardening and strain-rate hardening journal, December 1977

Shear band formation in plane strain compression journal, September 1988

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

A hyperelastic-based large strain elasto-plastic constitutive formulation with combined isotropic-kinematic hardening using the logarithmic stress and strain measures journal, October 1990

Hypo-Elasticity journal, January 1955

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

Conditions for the localization of deformation in pressure-sensitive dilatant materials journal, December 1975

Shear-Band Dynamics in Metallic Glasses journal, March 2015

Iterative Methods by Space Decomposition and Subspace Correction journal, December 1992

A Numerical Method for the Incompressible Navier-Stokes Equations Based on an Approximate Projection journal, March 1996

An Adaptive Level Set Approach for Incompressible Two-Phase Flows journal, January 1999

Shear bands in metallic glasses journal, April 2013

Strain localization in ductile single crystals journal, October 1977

Thickness of shear bands in metallic glasses journal, August 2006

Strain localization in amorphous metals journal, February 1982

A computational procedure for rate-independent crystal plasticity journal, April 1996

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

Kinematic description of crystal plasticity in the finite kinematic framework: A micromechanical understanding of F=FeFp journal, July 2014

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

Interfacial gauge methods for incompressible fluid dynamics journal, June 2016

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

Necking instabilities in elastoviscoplastic materials journal, July 2018

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

Bulk Metallic Glasses as Structural Materials: A Review: Bulk Metallic Glasses as Structural Materials: A Review
journal, May 2016

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

Shear-transformation-zone theory of linear glassy dynamics
journal, June 2011

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

Serrated flow and stick–slip deformation dynamics in the presence of shear-band interactions for a Zr-based metallic glass
journal, June 2012

Shear band formation in plane strain
journal, January 1981

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

An adaptive displacement/pressure finite element scheme for treating incompressibility effects in elasto-plastic materials
journal, January 2001

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

Thermodynamics of rate-independent plasticity
journal, March 2005

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

A second-order projection method for the incompressible navier-stokes equations
journal, December 1989

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

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

Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids
journal, July 1981

Tensile ductility and necking of metallic glass
journal, August 2007

Adaptive low Mach number simulations of nuclear flame microphysics
journal, April 2004

Mechanical behavior of amorphous alloys
journal, July 2007

On the analysis of rotation and stress rate in deforming bodies
journal, December 1979

A second order accurate projection method for the incompressible Navier–Stokes equations on non-graded adaptive grids
journal, December 2006

Bulk Metallic Glasses Deform via Slip Avalanches
journal, April 2014

Microstructural evolution and mechanical properties of dissimilar Al–Cu joints produced by friction stir welding
journal, October 2013

An Impulse-Based Approximation of Fluid Motion due to Boundary Forces
journal, February 1996

Dynamics of viscoplastic deformation in amorphous solids
journal, June 1998

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

Low Mach Number Modeling of Type Ia Supernovae. I. Hydrodynamics
journal, February 2006

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

Finite rotation effects in numerical integration of rate constitutive equations arising in large-deformation analysis
journal, December 1980

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

Open MPI: Goals, Concept, and Design of a Next Generation MPI Implementation
book, January 2004

Characterization of nanometer-scale defects in metallic glasses by quantitative high-resolution transmission electron microscopy
journal, March 2002

Bifurcation analysis of the onset of necking in an elastic/plastic cylinder under uniaxial tension
journal, January 1974

A single shear band in a metallic glass: Local core and wide soft zone
journal, October 2014

An elementary discussion of definitions of stress rate
journal, January 1961

Finite element analysis of surface instability in hypo-elastic solids
journal, February 1990

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

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

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

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

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

A new hybrid numerical scheme for modelling elastodynamics in unbounded media with near-source heterogeneities
journal, August 2017

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journal, March 1996

Softening Caused by Profuse Shear Banding in a Bulk Metallic Glass
journal, March 2006

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

Objective modeling of strain localization
journal, January 2002

A Multigrid Method on Non-Graded Adaptive Octree and Quadtree Cartesian Grids
journal, June 2012

Dynamics of Large-Scale Plastic Deformation and the Necking Instability in Amorphous Solids
journal, January 2003

Accurate Projection Methods for the Incompressible Navier–Stokes Equations
journal, April 2001

Elastoplasticity beyond small deformations
journal, March 2006

Strain localization in dry sheared granular materials: A compactivity-based approach
journal, August 2018

Shear band spacing under bending of Zr-based metallic glass plates
journal, May 2004

Some computational aspects of elastic-plastic large strain analysis
journal, January 1981

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

Linear and rotary friction welding review
journal, February 2016

Tensile instability and necking in materials with strain hardening and strain-rate hardening
journal, December 1977

Shear band formation in plane strain compression
journal, September 1988

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

A hyperelastic-based large strain elasto-plastic constitutive formulation with combined isotropic-kinematic hardening using the logarithmic stress and strain measures
journal, October 1990

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journal, January 1955

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journal, September 2017

Conditions for the localization of deformation in pressure-sensitive dilatant materials
journal, December 1975

Shear-Band Dynamics in Metallic Glasses
journal, March 2015

Iterative Methods by Space Decomposition and Subspace Correction
journal, December 1992

A Numerical Method for the Incompressible Navier-Stokes Equations Based on an Approximate Projection
journal, March 1996

An Adaptive Level Set Approach for Incompressible Two-Phase Flows
journal, January 1999

Shear bands in metallic glasses
journal, April 2013

Strain localization in ductile single crystals
journal, October 1977

Thickness of shear bands in metallic glasses
journal, August 2006

Strain localization in amorphous metals
journal, February 1982

A computational procedure for rate-independent crystal plasticity
journal, April 1996

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

Kinematic description of crystal plasticity in the finite kinematic framework: A micromechanical understanding of F=FeFp
journal, July 2014

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

Interfacial gauge methods for incompressible fluid dynamics
journal, June 2016

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

Necking instabilities in elastoviscoplastic materials
journal, July 2018

The Derivation and Numerical Solution of the Equations for Zero Mach Number Combustion
journal, January 1985

Origin of Intermittent Plastic Flow and Instability of Shear Band Sliding in Bulk Metallic Glasses
journal, May 2013

Compressible and incompressible fluids
journal, September 1982