# 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:

- 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}

}

DOI: 10.1063/1.2729503

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