skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Trust-region based return mapping algorithm for implicit integration of elastic-plastic constitutive models

Abstract

A new method for the solution of the non-linear equations forming the core of constitutive model integration is proposed. Specifically, the trust-region method that has been developed in the numerical optimization community is successfully modified for use in implicit integration of elastic-plastic models. Although attention here is restricted to these rate-independent formulations, the proposed approach holds substantial promise for adoption with models incorporating complex physics, multiple inelastic mechanisms, and/or multiphysics. As a first step, the non-quadratic Hosford yield surface is used as a representative case to investigate computationally challenging constitutive models. The theory and implementation are presented, discussed, and compared to other common integration schemes. Multiple boundary value problems are studied and used to verify the proposed algorithm and demonstrate the capabilities of this approach over more common methodologies. Robustness and speed are then investigated and compared to existing algorithms. As a result through these efforts, it is shown that the utilization of a trust-region approach leads to superior performance versus a traditional closest-point projection Newton-Raphson method and comparable speed and robustness to a line search augmented scheme.

Authors:
ORCiD logo [1];  [1]
  1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Publication Date:
Research Org.:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1343620
Report Number(s):
SAND-2016-11942J
Journal ID: ISSN 0029-5981; 649449
DOE Contract Number:  
AC04-94AL85000
Resource Type:
Journal Article
Journal Name:
International Journal for Numerical Methods in Engineering
Additional Journal Information:
Journal Volume: 112; Journal Issue: 3; Journal ID: ISSN 0029-5981
Publisher:
Wiley
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; constitutive model integration; return mapping algorithms; trust-region; Hosford yield surface

Citation Formats

Lester, Brian T., and Scherzinger, William M. Trust-region based return mapping algorithm for implicit integration of elastic-plastic constitutive models. United States: N. p., 2017. Web. doi:10.1002/nme.5515.
Lester, Brian T., & Scherzinger, William M. Trust-region based return mapping algorithm for implicit integration of elastic-plastic constitutive models. United States. doi:10.1002/nme.5515.
Lester, Brian T., and Scherzinger, William M. Thu . "Trust-region based return mapping algorithm for implicit integration of elastic-plastic constitutive models". United States. doi:10.1002/nme.5515. https://www.osti.gov/servlets/purl/1343620.
@article{osti_1343620,
title = {Trust-region based return mapping algorithm for implicit integration of elastic-plastic constitutive models},
author = {Lester, Brian T. and Scherzinger, William M.},
abstractNote = {A new method for the solution of the non-linear equations forming the core of constitutive model integration is proposed. Specifically, the trust-region method that has been developed in the numerical optimization community is successfully modified for use in implicit integration of elastic-plastic models. Although attention here is restricted to these rate-independent formulations, the proposed approach holds substantial promise for adoption with models incorporating complex physics, multiple inelastic mechanisms, and/or multiphysics. As a first step, the non-quadratic Hosford yield surface is used as a representative case to investigate computationally challenging constitutive models. The theory and implementation are presented, discussed, and compared to other common integration schemes. Multiple boundary value problems are studied and used to verify the proposed algorithm and demonstrate the capabilities of this approach over more common methodologies. Robustness and speed are then investigated and compared to existing algorithms. As a result through these efforts, it is shown that the utilization of a trust-region approach leads to superior performance versus a traditional closest-point projection Newton-Raphson method and comparable speed and robustness to a line search augmented scheme.},
doi = {10.1002/nme.5515},
journal = {International Journal for Numerical Methods in Engineering},
issn = {0029-5981},
number = 3,
volume = 112,
place = {United States},
year = {2017},
month = {1}
}

Works referenced in this record:

Line-search methods in general return mapping algorithms with application to porous plasticity
journal, January 2008

  • Seifert, T.; Schmidt, I.
  • International Journal for Numerical Methods in Engineering, Vol. 73, Issue 10
  • DOI: 10.1002/nme.2131

Orthotropic yield criterion for hexagonal closed packed metals
journal, July 2006


Plane stress yield function for aluminum alloy sheets—part II: FE formulation and its implementation
journal, March 2004


Linear transfomation-based anisotropic yield functions
journal, May 2005


Numerical technique in plasticity including solution advancement control
journal, March 1986

  • Runesson, Kenneth; Samuelsson, Alf; Bernspång, Lars
  • International Journal for Numerical Methods in Engineering, Vol. 22, Issue 3
  • DOI: 10.1002/nme.1620220315

Consistent linearization and finite element implementation of an incrementally objective canonical form return mapping algorithm for large deformation inelasticity
journal, August 2008

  • Seifert, T.; Maier, G.
  • International Journal for Numerical Methods in Engineering, Vol. 75, Issue 6
  • DOI: 10.1002/nme.2270

Prediction of six or eight ears in a drawn cup based on a new anisotropic yield function
journal, January 2006


Evaluation of stress integration algorithms for elastic–plastic constitutive models based on associated and non-associated flow rules
journal, October 2015

  • Safaei, Mohsen; Lee, Myoung-Gyu; De Waele, Wim
  • Computer Methods in Applied Mechanics and Engineering, Vol. 295
  • DOI: 10.1016/j.cma.2015.07.014

A Generalized Isotropic Yield Criterion
journal, June 1972

  • Hosford, W. F.
  • Journal of Applied Mechanics, Vol. 39, Issue 2
  • DOI: 10.1115/1.3422732

On linear transformations of stress tensors for the description of plastic anisotropy
journal, May 2007

  • Barlat, Frédéric; Yoon, Jeong Whan; Cazacu, Oana
  • International Journal of Plasticity, Vol. 23, Issue 5
  • DOI: 10.1016/j.ijplas.2006.10.001

A simplified canonical form algorithm with application to porous metal plasticity
journal, January 2005

  • Keavey, M. A.
  • International Journal for Numerical Methods in Engineering, Vol. 65, Issue 5
  • DOI: 10.1002/nme.1462

Efficient and modular algorithms in modeling finite inelastic deformations: Objective integration, parameter identification and sub-stepping techniques
journal, March 2007

  • Seifert, T.; Schenk, T.; Schmidt, I.
  • Computer Methods in Applied Mechanics and Engineering, Vol. 196, Issue 17-20
  • DOI: 10.1016/j.cma.2006.12.002

Path-dependent failure of inflated aluminum tubes
journal, November 2009


An accurate numerical algorithm for stress integration with finite rotations
journal, June 1987


On thermomechanics and transformation surfaces of polycrystalline NiTi shape memory alloy material
journal, January 2000


A criterion for description of anisotropy and yield differential effects in pressure-insensitive metals
journal, November 2004


Accuracy and stability of integration algorithms for elastoplastic constitutive relations
journal, September 1985

  • Ortiz, M.; Popov, E. P.
  • International Journal for Numerical Methods in Engineering, Vol. 21, Issue 9
  • DOI: 10.1002/nme.1620210902

A unified approach to finite deformation elastoplastic analysis based on the use of hyperelastic constitutive equations
journal, June 1985


Newton’s Method with a Model Trust Region Modification
journal, April 1982

  • Sorensen, D. C.
  • SIAM Journal on Numerical Analysis, Vol. 19, Issue 2
  • DOI: 10.1137/0719026

On the global convergence of trust region algorithms for unconstrained minimization
journal, July 1984


Elasto-plastic finite element method based on incremental deformation theory and continuum based shell elements for planar anisotropic sheet materials
journal, May 1999

  • Yoon, J. W.; Yang, D. Y.; Chung, K.
  • Computer Methods in Applied Mechanics and Engineering, Vol. 174, Issue 1-2
  • DOI: 10.1016/S0045-7825(98)00275-8

A general anisotropic yield criterion using bounds and a transformation weighting tensor
journal, December 1993


Operator split methods for the numerical solution of the elastoplastic dynamic problem
journal, August 1983

  • Ortiz, Miguel; Pinsky, Peter M.; Taylor, Robert L.
  • Computer Methods in Applied Mechanics and Engineering, Vol. 39, Issue 2
  • DOI: 10.1016/0045-7825(83)90018-X

Optimal control of the cylinder wake in the laminar regime by trust-region methods and POD reduced-order models
journal, August 2008


A smoothing trust-region Newton-CG method for minimax problem
journal, June 2008

  • Feng, Ye; Hongwei, Liu; Shuisheng, Zhou
  • Applied Mathematics and Computation, Vol. 199, Issue 2
  • DOI: 10.1016/j.amc.2007.10.070

A robust algorithm for finding the eigenvalues and eigenvectors of 3×3 symmetric matrices
journal, August 2008

  • Scherzinger, W. M.; Dohrmann, C. R.
  • Computer Methods in Applied Mechanics and Engineering, Vol. 197, Issue 45-48
  • DOI: 10.1016/j.cma.2008.03.031

Implicit integration procedure for viscoplastic Gurson materials
journal, September 2006

  • Betegón, C.; del Coz, J. J.; Peñuelas, I.
  • Computer Methods in Applied Mechanics and Engineering, Vol. 195, Issue 44-47
  • DOI: 10.1016/j.cma.2005.12.015

State update algorithm for isotropic elastoplasticity by incremental energy minimization: STATE UPDATE ALGORITHM FOR ISOTROPIC ELASTOPLASTICITY BY INCREMENTAL ENERGY MINIMIZATION
journal, July 2015

  • Nodargi, Nicola A.; Bisegna, Paolo
  • International Journal for Numerical Methods in Engineering, Vol. 105, Issue 3
  • DOI: 10.1002/nme.4966

Implicit algorithm for finite deformation hypoelastic–viscoplasticity in fcc metals
journal, January 2006

  • Voyiadjis, George Z.; Abed, Farid H.
  • International Journal for Numerical Methods in Engineering, Vol. 67, Issue 7
  • DOI: 10.1002/nme.1655

An analysis of a new class of integration algorithms for elastoplastic constitutive relations
journal, March 1986

  • Ortiz, M.; Simo, J. C.
  • International Journal for Numerical Methods in Engineering, Vol. 23, Issue 3
  • DOI: 10.1002/nme.1620230303

On the formulation of closest-point projection algorithms in elastoplasticity-part II: Globally convergent schemes: ELASTOPLASITICITY-PART II: GLOBALLY CONVERGENT SCHEMES
journal, October 2001

  • Pérez-Foguet, A.; Armero, F.
  • International Journal for Numerical Methods in Engineering, Vol. 53, Issue 2
  • DOI: 10.1002/nme.279

Time integration scheme for elastoplastic models based on anisotropic strain-rate potentials
journal, October 2009

  • Rabahallah, Meziane; Balan, Tudor; Bouvier, Salima
  • International Journal for Numerical Methods in Engineering, Vol. 80, Issue 3
  • DOI: 10.1002/nme.2640

Constitutive Modeling and Rupture Predictions of Al-6061-T6 Tubes Under Biaxial Loading Paths
journal, August 2010

  • Korkolis, Y. P.; Kyriakides, S.; Giagmouris, T.
  • Journal of Applied Mechanics, Vol. 77, Issue 6
  • DOI: 10.1115/1.4001940

A return mapping algorithm for isotropic and anisotropic plasticity models using a line search method
journal, April 2017


Recursive Trust-Region Methods for Multiscale Nonlinear Optimization
journal, January 2008

  • Gratton, Serge; Sartenaer, Annick; Toint, Philippe L.
  • SIAM Journal on Optimization, Vol. 19, Issue 1
  • DOI: 10.1137/050623012

Calculations of forming limit diagrams
journal, January 1990

  • Graf, Alejandro; Hosford, William F.
  • Metallurgical Transactions A, Vol. 21, Issue 1
  • DOI: 10.1007/BF02656427

Trust region methods for structural optimization using exact second order sensitivity
journal, August 1991

  • Sunar, M.; Belegundu, A. D.
  • International Journal for Numerical Methods in Engineering, Vol. 32, Issue 2
  • DOI: 10.1002/nme.1620320204

Inflation and burst of aluminum tubes. Part II: An advanced yield function including deformation-induced anisotropy
journal, September 2008


Universal anisotropic yield criterion based on superquadric functional representation: Part 1. Algorithmic issues and accuracy analysis
journal, January 1993

  • Dutko, Martin; Perić, Djordje; Owen, D. R. J.
  • Computer Methods in Applied Mechanics and Engineering, Vol. 109, Issue 1-2
  • DOI: 10.1016/0045-7825(93)90225-M

Levenberg–Marquardt vs Powell’s dogleg method for Gurson–Tvergaard–Needleman plasticity model
journal, September 2012

  • Shterenlikht, A.; Alexander, N. A.
  • Computer Methods in Applied Mechanics and Engineering, Vol. 237-240
  • DOI: 10.1016/j.cma.2012.04.018

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
  • DOI: 10.1002/nme.1620151210

Numerical implementation of a shape memory alloy thermomechanical constitutive model using return mapping algorithms
journal, February 2000


A return mapping algorithm for plane stress elastoplasticity
journal, March 1986

  • Simo, J. C.; Taylor, R. L.
  • International Journal for Numerical Methods in Engineering, Vol. 22, Issue 3
  • DOI: 10.1002/nme.1620220310