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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}
}