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Title: An Advanced Numerical Differentiation Scheme for Plastic Strain-Rate Computation

Abstract

Modern yield functions for orthotropic sheet metals are quite complex in a mathematical sense, mainly due to their non-quadratic character and/or the incorporation of eigenvalues of linearly transformed stress tensors (e.g. [5, 6]). In particular, the analytical computation of first and second order yield function gradients, which are, for instance, required in finite element codes, can become a very lengthy task. Thus, the numerical differentiation is a very convenient method to circumvent these difficulties. In the present article an advanced numerical differentation scheme is presented that exploits consequently the homogeneity property of the yield function.

Authors:
 [1]
  1. Hydro Aluminium Deutschland GmbH, Research and Development, Georg-von-Boeselager-Str. 21, D-53117 Bonn (Germany)
Publication Date:
OSTI Identifier:
21057002
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 907; Journal Issue: 1; Conference: 10. ESAFORM conference on material forming, Zaragoza (Spain), 18-20 Apr 2007; Other Information: DOI: 10.1063/1.2729503; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; ALLOYS; CALCULATION METHODS; EIGENVALUES; FINITE ELEMENT METHOD; METALS; PLASTICITY; STRAIN RATE; STRESSES; TENSORS

Citation Formats

Aretz, Holger. An Advanced Numerical Differentiation Scheme for Plastic Strain-Rate Computation. United States: N. p., 2007. Web. doi:10.1063/1.2729503.
Aretz, Holger. An Advanced Numerical Differentiation Scheme for Plastic Strain-Rate Computation. United States. doi:10.1063/1.2729503.
Aretz, Holger. Sat . "An Advanced Numerical Differentiation Scheme for Plastic Strain-Rate Computation". United States. doi:10.1063/1.2729503.
@article{osti_21057002,
title = {An Advanced Numerical Differentiation Scheme for Plastic Strain-Rate Computation},
author = {Aretz, Holger},
abstractNote = {Modern yield functions for orthotropic sheet metals are quite complex in a mathematical sense, mainly due to their non-quadratic character and/or the incorporation of eigenvalues of linearly transformed stress tensors (e.g. [5, 6]). In particular, the analytical computation of first and second order yield function gradients, which are, for instance, required in finite element codes, can become a very lengthy task. Thus, the numerical differentiation is a very convenient method to circumvent these difficulties. In the present article an advanced numerical differentation scheme is presented that exploits consequently the homogeneity property of the yield function.},
doi = {10.1063/1.2729503},
journal = {AIP Conference Proceedings},
number = 1,
volume = 907,
place = {United States},
year = {Sat Apr 07 00:00:00 EDT 2007},
month = {Sat Apr 07 00:00:00 EDT 2007}
}
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