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

Title: A method for smoothing multiple yield functions

Abstract

A method is presented that produces a single C2 differentiable and convex yield function from a plastic model that contains multiple yield surfaces that are individually C2 differentiable and convex. The method is suitable for implementation in numerical computer codes. Here, the error incurred through the smoothing procedure is quantified. The method is illustrated through a number of examples. Two simple finite-element models are solved to compare this method with existing approaches.

Authors:
ORCiD logo [1]; ORCiD logo [2];  [3];  [3]
  1. Queensland Centre for Advanced Technologies, Kenmore (Australia). Coal Mining Research Program
  2. Idaho National Lab. (INL), Idaho Falls, ID (United States). Fuel Modeling and Simulation
  3. Univ. of Southern California, Los Angeles, CA (United States). Sonny Astani Department of Civil and Environmental Engineering
Publication Date:
Research Org.:
Idaho National Lab. (INL), Idaho Falls, ID (United States)
Sponsoring Org.:
USDOE Office of Nuclear Energy (NE)
OSTI Identifier:
1575406
Alternate Identifier(s):
OSTI ID: 1570856
Report Number(s):
INL/JOU-19-52517-Rev000
Journal ID: ISSN 0029-5981; TRN: US2001213
Grant/Contract Number:  
AC07-05ID14517; NE0008438
Resource Type:
Accepted Manuscript
Journal Name:
International Journal for Numerical Methods in Engineering
Additional Journal Information:
Journal Volume: 2019; Journal ID: ISSN 0029-5981
Publisher:
Wiley
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; 42 ENGINEERING; Yield function; Plasticity; Return-map algorithm; Differentiability; Finite Element

Citation Formats

Wilkins, Andy, Spencer, Benjamin W., Jain, Amit, and Gencturk, Bora. A method for smoothing multiple yield functions. United States: N. p., 2019. Web. doi:10.1002/nme.6215.
Wilkins, Andy, Spencer, Benjamin W., Jain, Amit, & Gencturk, Bora. A method for smoothing multiple yield functions. United States. doi:10.1002/nme.6215.
Wilkins, Andy, Spencer, Benjamin W., Jain, Amit, and Gencturk, Bora. Wed . "A method for smoothing multiple yield functions". United States. doi:10.1002/nme.6215. https://www.osti.gov/servlets/purl/1575406.
@article{osti_1575406,
title = {A method for smoothing multiple yield functions},
author = {Wilkins, Andy and Spencer, Benjamin W. and Jain, Amit and Gencturk, Bora},
abstractNote = {A method is presented that produces a single C2 differentiable and convex yield function from a plastic model that contains multiple yield surfaces that are individually C2 differentiable and convex. The method is suitable for implementation in numerical computer codes. Here, the error incurred through the smoothing procedure is quantified. The method is illustrated through a number of examples. Two simple finite-element models are solved to compare this method with existing approaches.},
doi = {10.1002/nme.6215},
journal = {International Journal for Numerical Methods in Engineering},
number = ,
volume = 2019,
place = {United States},
year = {2019},
month = {9}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Citation Metrics:
Cited by: 2 works
Citation information provided by
Web of Science

Save / Share:

Works referenced in this record:

Detection of multiple active yield conditions for Mohr-Coulomb elasto-plasticity
journal, January 1997


Analytical CPP in energy-mapped stress space: Application to a modified Drucker–Prager yield surface
journal, January 2009

  • Crouch, Roger S.; Askes, Harm; Li, Tianbai
  • Computer Methods in Applied Mechanics and Engineering, Vol. 198, Issue 5-8
  • DOI: 10.1016/j.cma.2008.10.009

A robust return-map algorithm for general multisurface plasticity: A robust return-map algorithm for general multisurface plasticity
journal, June 2016

  • Adhikary, D. P.; Jayasundara, C. T.; Podgorney, R. K.
  • International Journal for Numerical Methods in Engineering, Vol. 109, Issue 2
  • DOI: 10.1002/nme.5284

Algorithmic issues for three-invariant hyperplastic Critical State models
journal, June 2011

  • Coombs, William M.; Crouch, Roger S.
  • Computer Methods in Applied Mechanics and Engineering, Vol. 200, Issue 25-28
  • DOI: 10.1016/j.cma.2011.03.019

An efficient return algorithm for non-associated plasticity with linear yield criteria in principal stress space
journal, December 2007


A C2 continuous approximation to the Mohr–Coulomb yield surface
journal, October 2011


NURBS plasticity: non-associated plastic flow
journal, July 2018

  • Coombs, William M.; Motlagh, Yousef Ghaffari
  • Computer Methods in Applied Mechanics and Engineering, Vol. 336
  • DOI: 10.1016/j.cma.2018.03.015

Discrete micromechanics of elastoplastic crystals
journal, November 1993

  • Borja, Ronaldo I.; Wren, Jon R.
  • International Journal for Numerical Methods in Engineering, Vol. 36, Issue 22
  • DOI: 10.1002/nme.1620362205

A comparative study of stress integration methods for the Barcelona Basic Model
journal, June 2012


Computational modelling of single crystals
journal, April 1993

  • Cuitino, A. M.; Ortiz, M.
  • Modelling and Simulation in Materials Science and Engineering, Vol. 1, Issue 3
  • DOI: 10.1088/0965-0393/1/3/001

Implicit Numerical Integration of Nonsmooth Multisurface Yield Criteria in the Principal Stress Space
journal, July 2013


Efficient return algorithms for associated plasticity with multiple yield planes
journal, January 2006

  • Clausen, J.; Damkilde, L.; Andersen, L.
  • International Journal for Numerical Methods in Engineering, Vol. 66, Issue 6
  • DOI: 10.1002/nme.1595

Physics-based multiscale coupling for full core nuclear reactor simulation
journal, October 2015


A smooth hyperbolic approximation to the Mohr-Coulomb yield criterion
journal, February 1995


NURBS plasticity: Yield surface evolution and implicit stress integration for isotropic hardening
journal, September 2017

  • Coombs, William M.; Ghaffari Motlagh, Yousef
  • Computer Methods in Applied Mechanics and Engineering, Vol. 324
  • DOI: 10.1016/j.cma.2017.05.017

Consistent tangent operators for rate-independent elastoplasticity
journal, February 1985


NURBS plasticity: Yield surface representation and implicit stress integration for isotropic inelasticity
journal, June 2016

  • Coombs, William M.; Petit, Oscar A.; Ghaffari Motlagh, Yousef
  • Computer Methods in Applied Mechanics and Engineering, Vol. 304
  • DOI: 10.1016/j.cma.2016.02.025

A composite plasticity model for concrete
journal, February 1996


Non-smooth multisurface plasticity and viscoplasticity. Loading/unloading conditions and numerical algorithms
journal, October 1988

  • Simo, J. C.; Kennedy, J. G.; Govindjee, S.
  • International Journal for Numerical Methods in Engineering, Vol. 26, Issue 10
  • DOI: 10.1002/nme.1620261003

An application of multisurface plasticity theory: yield surfaces of textured materials
journal, October 1996


On the implementation of inelastic constitutive equations with special reference to large deformation problems
journal, September 1982


Consistent tangent operators for rate-independent elastoplasticity
journal, January 1985