A return mapping algorithm for isotropic and anisotropic plasticity models using a line search method
Abstract
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.
- Authors:
-
- 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:
- 1323883
- Alternate Identifier(s):
- OSTI ID: 1339290; OSTI ID: 1340275; OSTI ID: 1413330
- Report Number(s):
- SAND-2016-4878J; SAND-2016-1575J; SAND-2016-11675J
Journal ID: ISSN 0045-7825; 640676
- Grant/Contract Number:
- AC04-94AL85000
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Computer Methods in Applied Mechanics and Engineering
- Additional Journal Information:
- Journal Name: Computer Methods in Applied Mechanics and Engineering; Journal ID: ISSN 0045-7825
- Publisher:
- Elsevier
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; 36 MATERIALS SCIENCE; plasticity; anisotropy; return mapping; line search
Citation Formats
Scherzinger, William M. A return mapping algorithm for isotropic and anisotropic plasticity models using a line search method. United States: N. p., 2016.
Web. doi:10.1016/j.cma.2016.11.026.
Scherzinger, William M. A return mapping algorithm for isotropic and anisotropic plasticity models using a line search method. United States. https://doi.org/10.1016/j.cma.2016.11.026
Scherzinger, William M. Sun .
"A return mapping algorithm for isotropic and anisotropic plasticity models using a line search method". United States. https://doi.org/10.1016/j.cma.2016.11.026. https://www.osti.gov/servlets/purl/1323883.
@article{osti_1323883,
title = {A return mapping algorithm for isotropic and anisotropic plasticity models using a line search method},
author = {Scherzinger, William M.},
abstractNote = {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.},
doi = {10.1016/j.cma.2016.11.026},
journal = {Computer Methods in Applied Mechanics and Engineering},
number = ,
volume = ,
place = {United States},
year = {Sun May 01 00:00:00 EDT 2016},
month = {Sun May 01 00:00:00 EDT 2016}
}
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Works referencing / citing this record:
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Regularized Yield Surfaces for Crystal Plasticity of Metals
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