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Title: Trust-region based return mapping algorithm for implicit integration of elastic-plastic constitutive models

Abstract

A new method for the solution of the non-linear equations forming the core of constitutive model integration is proposed. Specifically, the trust-region method that has been developed in the numerical optimization community is successfully modified for use in implicit integration of elastic-plastic models. Although attention here is restricted to these rate-independent formulations, the proposed approach holds substantial promise for adoption with models incorporating complex physics, multiple inelastic mechanisms, and/or multiphysics. As a first step, the non-quadratic Hosford yield surface is used as a representative case to investigate computationally challenging constitutive models. The theory and implementation are presented, discussed, and compared to other common integration schemes. Multiple boundary value problems are studied and used to verify the proposed algorithm and demonstrate the capabilities of this approach over more common methodologies. Robustness and speed are then investigated and compared to existing algorithms. As a result through these efforts, it is shown that the utilization of a trust-region approach leads to superior performance versus a traditional closest-point projection Newton-Raphson method and comparable speed and robustness to a line search augmented scheme.

Authors:
ORCiD logo [1];  [1]
  1. 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:
1343620
Report Number(s):
SAND-2016-11942J
Journal ID: ISSN 0029-5981; 649449
DOE Contract Number:
AC04-94AL85000
Resource Type:
Journal Article
Resource Relation:
Journal Name: International Journal for Numerical Methods in Engineering
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; constitutive model integration; return mapping algorithms; trust-region; Hosford yield surface

Citation Formats

Lester, Brian T., and Scherzinger, William M. Trust-region based return mapping algorithm for implicit integration of elastic-plastic constitutive models. United States: N. p., 2017. Web. doi:10.1002/nme.5515.
Lester, Brian T., & Scherzinger, William M. Trust-region based return mapping algorithm for implicit integration of elastic-plastic constitutive models. United States. doi:10.1002/nme.5515.
Lester, Brian T., and Scherzinger, William M. Thu . "Trust-region based return mapping algorithm for implicit integration of elastic-plastic constitutive models". United States. doi:10.1002/nme.5515. https://www.osti.gov/servlets/purl/1343620.
@article{osti_1343620,
title = {Trust-region based return mapping algorithm for implicit integration of elastic-plastic constitutive models},
author = {Lester, Brian T. and Scherzinger, William M.},
abstractNote = {A new method for the solution of the non-linear equations forming the core of constitutive model integration is proposed. Specifically, the trust-region method that has been developed in the numerical optimization community is successfully modified for use in implicit integration of elastic-plastic models. Although attention here is restricted to these rate-independent formulations, the proposed approach holds substantial promise for adoption with models incorporating complex physics, multiple inelastic mechanisms, and/or multiphysics. As a first step, the non-quadratic Hosford yield surface is used as a representative case to investigate computationally challenging constitutive models. The theory and implementation are presented, discussed, and compared to other common integration schemes. Multiple boundary value problems are studied and used to verify the proposed algorithm and demonstrate the capabilities of this approach over more common methodologies. Robustness and speed are then investigated and compared to existing algorithms. As a result through these efforts, it is shown that the utilization of a trust-region approach leads to superior performance versus a traditional closest-point projection Newton-Raphson method and comparable speed and robustness to a line search augmented scheme.},
doi = {10.1002/nme.5515},
journal = {International Journal for Numerical Methods in Engineering},
number = ,
volume = ,
place = {United States},
year = {Thu Jan 19 00:00:00 EST 2017},
month = {Thu Jan 19 00:00:00 EST 2017}
}
  • Here, a new method for the solution of the non-linear equations forming the core of constitutive model integration is proposed. Specifically, the trust-region method that has been developed in the numerical optimization community is successfully modified for use in implicit integration of elastic-plastic models. Although attention here is restricted to these rate-independent formulations, the proposed approach holds substantial promise for adoption with models incorporating complex physics, multiple inelastic mechanisms, and/or multiphysics. As a first step, the non-quadratic Hosford yield surface is used as a representative case to investigate computationally challenging constitutive models. The theory and implementation are presented, discussed, andmore » compared to other common integration schemes. Multiple boundary value problems are studied and used to verify the proposed algorithm and demonstrate the capabilities of this approach over more common methodologies. Robustness and speed are then investigated and compared to existing algorithms. Through these efforts, it is shown that the utilization of a trust-region approach leads to superior performance versus a traditional closest-point projection Newton-Raphson method and comparable speed and robustness to a line search augmented scheme.« less
  • Here, a new method for the solution of the non-linear equations forming the core of constitutive model integration is proposed. Specifically, the trust-region method that has been developed in the numerical optimization community is successfully modified for use in implicit integration of elastic-plastic models. Although attention here is restricted to these rate-independent formulations, the proposed approach holds substantial promise for adoption with models incorporating complex physics, multiple inelastic mechanisms, and/or multiphysics. As a first step, the non-quadratic Hosford yield surface is used as a representative case to investigate computationally challenging constitutive models. The theory and implementation are presented, discussed, andmore » compared to other common integration schemes. Multiple boundary value problems are studied and used to verify the proposed algorithm and demonstrate the capabilities of this approach over more common methodologies. Robustness and speed are then investigated and compared to existing algorithms. Through these efforts, it is shown that the utilization of a trust-region approach leads to superior performance versus a traditional closest-point projection Newton-Raphson method and comparable speed and robustness to a line search augmented scheme.« less
  • 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 J 2, 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 amore » 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.« less
  • Abstract not provided.
  • 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. Here, most plasticity models implemented in computational codes use an isotropic von Mises yield surface. The von Mises, of J 2, yield surface has a simple predictor-corrector algorithm - the radial return algorithm - to integrate the model.