A robust return-map algorithm for general multisurface plasticity

Adhikary, Deepak P.; Jayasundara, Chandana T.; Podgorney, Robert K.; Wilkins, Andy H.

doi:10.1002/nme.5284

Title: A robust return-map algorithm for general multisurface plasticity

Journal Article · Thu Jun 16 00:00:00 EDT 2016 · International Journal for Numerical Methods in Engineering

DOI:https://doi.org/10.1002/nme.5284· OSTI ID:1259311

Adhikary, Deepak P. ^[1]; Jayasundara, Chandana T. ^[1]; Podgorney, Robert K. ^[2]; Wilkins, Andy H. ^[1]

CSIRO Energy Flagship, Queensland Centre for Advanced Technologies, Kenmore (Australia)
Idaho National Lab. (INL), Idaho Falls, ID (United States)

Three new contributions to the field of multisurface plasticity are presented for general situations with an arbitrary number of nonlinear yield surfaces with hardening or softening. A method for handling linearly dependent flow directions is described. A residual that can be used in a line search is defined. An algorithm that has been implemented and comprehensively tested is discussed in detail. Examples are presented to illustrate the computational cost of various components of the algorithm. The overall result is that a single Newton-Raphson iteration of the algorithm costs between 1.5 and 2 times that of an elastic calculation. Examples also illustrate the successful convergence of the algorithm in complicated situations. For example, without using the new contributions presented here, the algorithm fails to converge for approximately 50% of the trial stresses for a common geomechanical model of sedementary rocks, while the current algorithm results in complete success. Since it involves no approximations, the algorithm is used to quantify the accuracy of an efficient, pragmatic, but approximate, algorithm used for sedimentary-rock plasticity in a commercial software package. Furthermore, the main weakness of the algorithm is identified as the difficulty of correctly choosing the set of initially active constraints in the general setting.

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Research Organization:: Idaho National Laboratory (INL), Idaho Falls, ID (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC07-05ID14517

OSTI ID:: 1259311

Report Number(s):: INL/JOU-15-34725

Journal Information:: International Journal for Numerical Methods in Engineering, Journal Name: International Journal for Numerical Methods in Engineering; ISSN 0029-5981

Publisher:: WileyCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 23 works

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References (23)

A composite plasticity model for concrete Feenstra, Peter H.; De Borst, René International Journal of Solids and Structures, Vol. 33, Issue 5 https://doi.org/10.1016/0020-7683(95)00060-N	journal	February 1996
Efficient return algorithms for associated plasticity with multiple yield planes Clausen, J.; Damkilde, L.; Andersen, L. International Journal for Numerical Methods in Engineering, Vol. 66, Issue 6 https://doi.org/10.1002/nme.1595	journal	January 2006
An efficient return algorithm for non-associated plasticity with linear yield criteria in principal stress space Clausen, Johan; Damkilde, Lars; Andersen, Lars Computers & Structures, Vol. 85, Issue 23-24 https://doi.org/10.1016/j.compstruc.2007.04.002	journal	December 2007
Implicit Numerical Integration of Nonsmooth Multisurface Yield Criteria in the Principal Stress Space Karaoulanis, Fotios E. Archives of Computational Methods in Engineering, Vol. 20, Issue 3 https://doi.org/10.1007/s11831-013-9087-3	journal	July 2013
Detection of multiple active yield conditions for Mohr-Coulomb elasto-plasticity Computers & Structures, Vol. 62, Issue 1 https://doi.org/10.1016/S0045-7949(96)00267-2	journal	January 1997
A C2 continuous approximation to the Mohr–Coulomb yield surface Abbo, A. J.; Lyamin, A. V.; Sloan, S. W. International Journal of Solids and Structures, Vol. 48, Issue 21 https://doi.org/10.1016/j.ijsolstr.2011.06.021	journal	October 2011
Non-smooth multisurface plasticity and viscoplasticity. Loading/unloading conditions and numerical algorithms Simo, J. C.; Kennedy, J. G.; Govindjee, S. International Journal for Numerical Methods in Engineering, Vol. 26, Issue 10 https://doi.org/10.1002/nme.1620261003	journal	October 1988
Computational Inelasticity Simo, J. C.; Hughes, T. J. R. Interdisciplinary Applied Mathematics https://doi.org/10.1007/b98904	book	January 1998
Corners in plasticity—Koiter's theory revisited Ottosen, Niels Saabye; Ristinmaa, Matti International Journal of Solids and Structures, Vol. 33, Issue 25 https://doi.org/10.1016/0020-7683(95)00207-3	journal	October 1996
Discrete micromechanics of elastoplastic crystals Borja, Ronaldo I.; Wren, Jon R. International Journal for Numerical Methods in Engineering, Vol. 36, Issue 22 https://doi.org/10.1002/nme.1620362205	journal	November 1993
Computational modelling of single crystals Cuitino, A. M.; Ortiz, M. Modelling and Simulation in Materials Science and Engineering, Vol. 1, Issue 3 https://doi.org/10.1088/0965-0393/1/3/001	journal	April 1993
An application of multisurface plasticity theory: yield surfaces of textured materials Maudlin, P. J.; Wright, S. I.; Kocks, U. F. Acta Materialia, Vol. 44, Issue 10 https://doi.org/10.1016/S1359-6454(96)00039-0	journal	October 1996
Modelling and computation of instability phenomena in multisurface elasto-plasticity Sawischlewski, E.; Steinmann, P.; Stein, E. Computational Mechanics, Vol. 18, Issue 4 https://doi.org/10.1007/BF00364140	journal	July 1996
Aspects of non-associated single crystal plasticity: Influence of non-schmid effects and localization analysis Steinmann, P.; Kuhl, E.; Stein, E. International Journal of Solids and Structures, Vol. 35, Issue 33 https://doi.org/10.1016/S0020-7683(97)00241-2	journal	November 1998
Rate-independent crystalline and polycrystalline plasticity, application to FCC materials Knockaert, R.; Chastel, Y.; Massoni, E. International Journal of Plasticity, Vol. 16, Issue 2 https://doi.org/10.1016/S0749-6419(99)00071-6	journal	January 2000
On the uniqueness of a rate-independent plasticity model for single crystals Zuo, Q. H. International Journal of Plasticity, Vol. 27, Issue 8 https://doi.org/10.1016/j.ijplas.2010.12.002	journal	August 2011
Implicit integration of composite yield surfaces with corners Pramono, Eddy; Willam, Kaspar Engineering Computations, Vol. 6, Issue 3 https://doi.org/10.1108/eb023774	journal	March 1989
MOOSE: A parallel computational framework for coupled systems of nonlinear equations Gaston, Derek; Newman, Chris; Hansen, Glen Nuclear Engineering and Design, Vol. 239, Issue 10 https://doi.org/10.1016/j.nucengdes.2009.05.021	journal	October 2009
Convex Optimization Boyd, Stephen; Vandenberghe, Lieven https://doi.org/10.1017/CBO9780511804441	book	January 2004
A computational procedure for rate-independent crystal plasticity Anand, L.; Kothari, M. Journal of the Mechanics and Physics of Solids, Vol. 44, Issue 4 https://doi.org/10.1016/0022-5096(96)00001-4	journal	April 1996
Implicit numerical integration of a three-invariant, isotropic/kinematic hardening cap plasticity model for geomaterials Foster, C. D.; Regueiro, R. A.; Fossum, A. F. Computer Methods in Applied Mechanics and Engineering, Vol. 194, Issue 50-52 https://doi.org/10.1016/j.cma.2005.01.001	journal	December 2005
Shear and compaction band formation on an elliptic yield cap Rudnicki, John W. Journal of Geophysical Research, Vol. 109, Issue B3 https://doi.org/10.1029/2003JB002633	journal	January 2004
Consistent tangent operators for constitutive rate equations Fellin, Wolfgang; Ostermann, Alexander International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 26, Issue 12 https://doi.org/10.1002/nag.242	journal	January 2002

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Title: A robust return-map algorithm for general multisurface plasticity

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