A return mapping algorithm for isotropic and anisotropic plasticity models using a line search method

Scherzinger, William M.

doi:10.1016/j.cma.2016.11.026

Title: A return mapping algorithm for isotropic and anisotropic plasticity models using a line search method

Journal Article · Sun May 01 00:00:00 EDT 2016 · Computer Methods in Applied Mechanics and Engineering

DOI:https://doi.org/10.1016/j.cma.2016.11.026· OSTI ID:1323883

Scherzinger, William M. ^[1]

Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

The numerical integration of constitutive models in computational solid mechanics codes allows for the solution of boundary value problems involving complex material behavior. Metal plasticity models, in particular, have been instrumental in the development of these codes. Most plasticity models implemented in computational codes use an isotropic von Mises yield surface. The von Mises, or J₂, model uses a predictor–corrector algorithm–the radial return algorithm–to integrate the model. For non-quadratic yield surfaces, including anisotropic yield surfaces, no simple algorithm exists. This paper presents and analyzes a line search algorithm for the return mapping problem that shows excellent improvement over a Newton–Raphson model. Two non-quadratic yield surfaces–one isotropic and one anisotropic–are studied in this paper. The line search algorithm used for integrating the models is shown to be reliable and robust. The theory and implementation of the models, the details of the return mapping algorithm, and results that show the effectiveness of the method are presented. Lastly, a few simple boundary value problems verify the implementation and show the impact of the models. For the internal pressurization of a cylinder, the importance of modeling anisotropy correctly is shown.

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Research Organization:: Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC04-94AL85000

OSTI ID:: 1323883

Alternate ID(s):: OSTI ID: 1339290; OSTI ID: 1340275; OSTI ID: 1413330

Report Number(s):: SAND-2016-4878J; SAND-2016-1575J; SAND-2016-11675J; 640676

Journal Information:: Computer Methods in Applied Mechanics and Engineering, Journal Name: Computer Methods in Applied Mechanics and Engineering; ISSN 0045-7825

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 37 works

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Implementation issues of Yld2000-2d model under larger biaxial yield stress Zhang, Yong; Zhang, Qing; Sun, Yuantao Mechanics & Industry, Vol. 19, Issue 5 https://doi.org/10.1051/meca/2018031	journal	January 2018
Sandia Fracture Challenge 3: detailing the Sandia Team Q failure prediction strategy Karlson, Kyle N.; Alleman, Coleman; Foulk III, James W. International Journal of Fracture, Vol. 218, Issue 1-2 https://doi.org/10.1007/s10704-019-00365-x	journal	July 2019
Generalized radial-return mapping algorithm for anisotropic von Mises plasticity framed in material eigenspace: Generalized radial-return mapping algorithm Versino, Daniele; Bennett, Kane C. International Journal for Numerical Methods in Engineering, Vol. 116, Issue 3 https://doi.org/10.1002/nme.5921	journal	August 2018
Regularized Yield Surfaces for Crystal Plasticity of Metals Holmedal, Bjørn Crystals, Vol. 10, Issue 12 https://doi.org/10.3390/cryst10121076	journal	November 2020

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36 MATERIALS SCIENCE
plasticity
anisotropy
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Title: A return mapping algorithm for isotropic and anisotropic plasticity models using a line search method

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