Finite element formulation with embedded weak discontinuities for strain localization under dynamic conditions

Jin, Tao; Mourad, Hashem M.; Bronkhorst, Curt A.; Livescu, Veronica

doi:10.1007/s00466-017-1470-8

Title: Finite element formulation with embedded weak discontinuities for strain localization under dynamic conditions

Abstract

Here, we present an explicit finite element formulation designed for the treatment of strain localization under highly dynamic conditions. We also used a material stability analysis to detect the onset of localization behavior. Finite elements with embedded weak discontinuities are employed with the aim of representing subsequent localized deformation accurately. The formulation and its algorithmic implementation are described in detail. Numerical results are presented to illustrate the usefulness of this computational framework in the treatment of strain localization under highly dynamic conditions, and to examine its performance characteristics in the context of two-dimensional plane-strain problems.

Authors:

Jin, Tao ^[1];

^[1];

^[1]

Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Publication Date:: Wed Sep 13 00:00:00 EDT 2017

Research Org.:: Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1407880

Report Number(s):: LA-UR-17-20920
Journal ID: ISSN 0178-7675; TRN: US1702926

Grant/Contract Number:: AC52-06NA25396

Resource Type:: Accepted Manuscript

Journal Name:: Computational Mechanics

Additional Journal Information:: Journal Volume: 61; Journal Issue: 1-2; Journal ID: ISSN 0178-7675

Publisher:: Springer

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING; 36 MATERIALS SCIENCE; strain localization; adiabatic shear banding; finite element method; enhanced strain methods; explicit dynamic analysis; viscoplasticity; dynamic recrystallization

Citation Formats


                    Jin, Tao, Mourad, Hashem M., Bronkhorst, Curt A., and Livescu, Veronica. Finite element formulation with embedded weak discontinuities for strain localization under dynamic conditions.  United States: N. p., 2017. 
Web.  doi:10.1007/s00466-017-1470-8.

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                    Jin, Tao, Mourad, Hashem M., Bronkhorst, Curt A., & Livescu, Veronica. Finite element formulation with embedded weak discontinuities for strain localization under dynamic conditions.  United States.  https://doi.org/10.1007/s00466-017-1470-8

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                    Jin, Tao, Mourad, Hashem M., Bronkhorst, Curt A., and Livescu, Veronica. Wed .  
"Finite element formulation with embedded weak discontinuities for strain localization under dynamic conditions".  United States.  https://doi.org/10.1007/s00466-017-1470-8.  https://www.osti.gov/servlets/purl/1407880.

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@article{osti_1407880,

  title        = {Finite element formulation with embedded weak discontinuities for strain localization under dynamic conditions},

  author       = {Jin, Tao and Mourad, Hashem M. and Bronkhorst, Curt A. and Livescu, Veronica},

  abstractNote = {Here, we present an explicit finite element formulation designed for the treatment of strain localization under highly dynamic conditions. We also used a material stability analysis to detect the onset of localization behavior. Finite elements with embedded weak discontinuities are employed with the aim of representing subsequent localized deformation accurately. The formulation and its algorithmic implementation are described in detail. Numerical results are presented to illustrate the usefulness of this computational framework in the treatment of strain localization under highly dynamic conditions, and to examine its performance characteristics in the context of two-dimensional plane-strain problems.},

  doi          = {10.1007/s00466-017-1470-8},

  journal      = {Computational Mechanics},

  number       = 1-2,

  volume       = 61,

  place        = {United States},

  year         = {Wed Sep 13 00:00:00 EDT 2017},

  month        = {Wed Sep 13 00:00:00 EDT 2017}

}

Copy to clipboard

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Title: Finite element formulation with embedded weak discontinuities for strain localization under dynamic conditions

Abstract

Citation Formats

Incrementally objective implicit integration of hypoelastic–viscoplastic constitutive equations based on the mechanical threshold strength model journal, October 2013

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An analysis of strong discontinuities induced by strain-softening in rate-independent inelastic solids journal, January 1993

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Shear band formation in thermal viscoplastic materials journal, August 1989

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Dynamically propagating shear bands in impact-loaded prenotched plates—I. Experimental investigations of temperature signatures and propagation speed journal, June 1996

A finite thickness band method for ductile fracture analysis journal, December 2009

Analysis of the cup-cone fracture in a round tensile bar journal, January 1984

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Acceleration waves in solids journal, January 1962

Influence of shock prestraining on the formation of shear localization in 304 stainless steel journal, June 2005

Low-temperature and high-strain-rate deformation of nickel and nickel-carbon alloys and analysis of the constitutive behavior according to an internal state variable model journal, July 1990

Extended finite element method in computational fracture mechanics: a retrospective examination journal, November 2015

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

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A finite element with embedded localization zones journal, September 1988

A constitutive description of the deformation of copper based on the use of the mechanical threshold stress as an internal state variable journal, January 1988

An experimental and numerical study of the localization behavior of tantalum and stainless steel journal, July 2006

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Three-dimensional finite elements with embedded strong discontinuities to model material failure in the infinitesimal range: 3D FINITE ELEMENTS WITH EMBEDDED STRONG DISCONTINUITIES journal, June 2012

Elements with embedded localization zones for large deformation problems journal, January 1988

An analysis of strong discontinuities in multiplicative finite strain plasticity and their relation with the numerical simulation of strain localization in solids journal, August 1996

The respective influence of microstructural and thermal softening on adiabatic shear localization journal, January 2013

A finite element with a unidirectionally enriched strain field for localization analysis journal, January 1990

Modelling Strong Discontinuities in Solid Mechanics via Strain Softening Constitutive Equations. part 2: Numerical Simulation journal, November 1996

Analytical Characterization of Shear Localization in Thermoviscoplastic Materials journal, December 1987

Finite elements with embedded strong discontinuities for the modeling of failure in solids journal, January 2007

Isogeometric analysis of shear bands journal, March 2014

Numerical simulation of dynamic fracture using finite elements with embedded discontinuities journal, October 2009

On criteria for dynamic adiabatic shear band propagation journal, July 2007

Modeling and simulation framework for dynamic strain localization in elasto-viscoplastic metallic materials subject to large deformations journal, January 2017

A variational multiscale approach to strain localization – formulation for multidimensional problems journal, July 2000

The initiation and growth of adiabatic shear bands journal, January 1985

Comparative study on finite elements with embedded discontinuities journal, July 2000

On the Variational Foundations of Assumed Strain Methods journal, March 1986

New finite elements with embedded strong discontinuities in the finite deformation range journal, June 2008

Efficient implementation of quadrilaterals with high coarse-mesh accuracy journal, March 1986

Modelling Strong Discontinuities in Solid Mechanics via Strain Softening Constitutive Equations. part 1: Fundamentals journal, November 1996

Thermal softening induced plastic instability in rate-dependent materials journal, April 2009

Advances in the numerical treatment of grain-boundary migration: Coupling with mass transport and mechanics journal, December 2006

Microstructural evolution in adiabatic shear band in the ultrafine-grained austenitic stainless steel processed by multi-axial compression journal, August 2014

High resolution two-dimensional shear band computations: imperfections and mesh dependence journal, November 1994

Incrementally objective implicit integration of hypoelastic–viscoplastic constitutive equations based on the mechanical threshold strength model
journal, October 2013

Onset of shear localization in viscoplastic solids
journal, January 1987

A comparative study on finite elements for capturing strong discontinuities: E-FEM vs X-FEM
journal, July 2006

Dynamic shear band propagation and micro-structure of adiabatic shear band
journal, November 2001

An analysis of strong discontinuities induced by strain-softening in rate-independent inelastic solids
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A study of strain localization in a multiple scale framework—The one-dimensional problem
journal, July 1998

Strain heating and thermal softening in continental shear zones: a review
journal, January 1980

Modeling three-dimensional crack propagation-A comparison of crack path tracking strategies
journal, November 2008

An EBSD investigation on deformation-induced shear bands in a low nickel austenitic stainless steel under controlled shock-loading conditions
journal, July 2014

A finite element method for localized failure analysis
journal, March 1987

Extended embedded finite elements with continuous displacement jumps for the modeling of localized failure in solids
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Shear band formation in thermal viscoplastic materials
journal, August 1989

Dynamic Recrystallization as a Potential Cause for Adiabatic Shear Failure
journal, October 2008

Generalization of selective integration procedures to anisotropic and nonlinear media
journal, September 1980

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journal, February 2006

Mesh-free Galerkin simulations of dynamic shear band propagation and failure mode transition
journal, March 2002

Dynamically propagating shear bands in impact-loaded prenotched plates—I. Experimental investigations of temperature signatures and propagation speed
journal, June 1996

A finite thickness band method for ductile fracture analysis
journal, December 2009

Analysis of the cup-cone fracture in a round tensile bar
journal, January 1984

Continuum modelling of strong discontinuities in solid mechanics using damage models
journal, December 1995

Acceleration waves in solids
journal, January 1962

Influence of shock prestraining on the formation of shear localization in 304 stainless steel
journal, June 2005

Low-temperature and high-strain-rate deformation of nickel and nickel-carbon alloys and analysis of the constitutive behavior according to an internal state variable model
journal, July 1990

Extended finite element method in computational fracture mechanics: a retrospective examination
journal, November 2015

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

Growth of nuclei in a cellular automaton simulation of recrystallisation
journal, January 1997

A finite element with embedded localization zones
journal, September 1988

A constitutive description of the deformation of copper based on the use of the mechanical threshold stress as an internal state variable
journal, January 1988

An experimental and numerical study of the localization behavior of tantalum and stainless steel
journal, July 2006

Assumed enhanced strain and the extended finite element methods: A unification of concepts
journal, June 2008

Three-dimensional finite elements with embedded strong discontinuities to model material failure in the infinitesimal range: 3D FINITE ELEMENTS WITH EMBEDDED STRONG DISCONTINUITIES
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Elements with embedded localization zones for large deformation problems
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Analytical Characterization of Shear Localization in Thermoviscoplastic Materials
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Isogeometric analysis of shear bands
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Numerical simulation of dynamic fracture using finite elements with embedded discontinuities
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A variational multiscale approach to strain localization – formulation for multidimensional problems
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The initiation and growth of adiabatic shear bands
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Comparative study on finite elements with embedded discontinuities
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On the Variational Foundations of Assumed Strain Methods
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New finite elements with embedded strong discontinuities in the finite deformation range
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Efficient implementation of quadrilaterals with high coarse-mesh accuracy
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Modelling Strong Discontinuities in Solid Mechanics via Strain Softening Constitutive Equations. part 1: Fundamentals
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Thermal softening induced plastic instability in rate-dependent materials
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Advances in the numerical treatment of grain-boundary migration: Coupling with mass transport and mechanics
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Microstructural evolution in adiabatic shear band in the ultrafine-grained austenitic stainless steel processed by multi-axial compression
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High resolution two-dimensional shear band computations: imperfections and mesh dependence
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