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Title: Generalized radial-return mapping algorithm for anisotropic von Mises plasticity framed in material eigenspace

Abstract

A computationally efficient integration algorithm for anisotropic plasticity is proposed, which is identified as a generalization of the radial-return mapping algorithm to anisotropy. The algorithm is based upon formulation within the eigenspace of a material anisotropy tensor associated with anisotropic quadratic von Mises (J 2) plasticity (also called Hill plasticity), for which it is shown to ensure that the flow rule remains associative, ie, the normality condition is satisfied. Extension of the algorithm to include anisotropic elasticity (anisotropic elastoplasticity) is further provided, made possible by the identification of a certain fourth-order material tensor dependent on both the elastic and plastic anisotropy. The derivation of the fully elastoplastically anisotropic algorithm involves further complexity, but the resulting algorithm is shown to closely resemble the purely plastically anisotropic one once the appropriate eigenspace is identified. The proposed generalized radial-return algorithm is compared to a classical closest-point projection algorithm, for which it is shown to provide considerable advantage in computational cost. In conclusion, the efficiency, accuracy, and robustness of the algorithm are demonstrated through various illustrative test cases and in the finite element simulation of Taylor impact tests on tantalum.

Authors:
 [1]; ORCiD logo [1]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1481138
Alternate Identifier(s):
OSTI ID: 1463918
Report Number(s):
LA-UR-17-30973
Journal ID: ISSN 0029-5981
Grant/Contract Number:  
AC52-06NA25396
Resource Type:
Accepted Manuscript
Journal Name:
International Journal for Numerical Methods in Engineering
Additional Journal Information:
Journal Volume: 116; Journal Issue: 3; Journal ID: ISSN 0029-5981
Publisher:
Wiley
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; 36 MATERIALS SCIENCE; algorithm efficiency; anisotropy; elastoplasticity; finite element method; return mapping; von Mises

Citation Formats

Versino, Daniele, and Bennett, Kane C. Generalized radial-return mapping algorithm for anisotropic von Mises plasticity framed in material eigenspace. United States: N. p., 2018. Web. doi:10.1002/nme.5921.
Versino, Daniele, & Bennett, Kane C. Generalized radial-return mapping algorithm for anisotropic von Mises plasticity framed in material eigenspace. United States. doi:10.1002/nme.5921.
Versino, Daniele, and Bennett, Kane C. Tue . "Generalized radial-return mapping algorithm for anisotropic von Mises plasticity framed in material eigenspace". United States. doi:10.1002/nme.5921. https://www.osti.gov/servlets/purl/1481138.
@article{osti_1481138,
title = {Generalized radial-return mapping algorithm for anisotropic von Mises plasticity framed in material eigenspace},
author = {Versino, Daniele and Bennett, Kane C.},
abstractNote = {A computationally efficient integration algorithm for anisotropic plasticity is proposed, which is identified as a generalization of the radial-return mapping algorithm to anisotropy. The algorithm is based upon formulation within the eigenspace of a material anisotropy tensor associated with anisotropic quadratic von Mises (J2) plasticity (also called Hill plasticity), for which it is shown to ensure that the flow rule remains associative, ie, the normality condition is satisfied. Extension of the algorithm to include anisotropic elasticity (anisotropic elastoplasticity) is further provided, made possible by the identification of a certain fourth-order material tensor dependent on both the elastic and plastic anisotropy. The derivation of the fully elastoplastically anisotropic algorithm involves further complexity, but the resulting algorithm is shown to closely resemble the purely plastically anisotropic one once the appropriate eigenspace is identified. The proposed generalized radial-return algorithm is compared to a classical closest-point projection algorithm, for which it is shown to provide considerable advantage in computational cost. In conclusion, the efficiency, accuracy, and robustness of the algorithm are demonstrated through various illustrative test cases and in the finite element simulation of Taylor impact tests on tantalum.},
doi = {10.1002/nme.5921},
journal = {International Journal for Numerical Methods in Engineering},
number = 3,
volume = 116,
place = {United States},
year = {2018},
month = {7}
}

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