## Generalized radial-return mapping algorithm for anisotropic von Mises plasticity framed in material eigenspace

## Abstract

A computationally efficient integration algorithm for anisotropic plasticity is proposed, which is identified as a generalization of the radial-return mapping algorithm to anisotropy. The algorithm is based upon formulation within the eigenspace of a material anisotropy tensor associated with anisotropic quadratic von Mises (J _{2}) plasticity (also called Hill plasticity), for which it is shown to ensure that the flow rule remains associative, ie, the normality condition is satisfied. Extension of the algorithm to include anisotropic elasticity (anisotropic elastoplasticity) is further provided, made possible by the identification of a certain fourth-order material tensor dependent on both the elastic and plastic anisotropy. The derivation of the fully elastoplastically anisotropic algorithm involves further complexity, but the resulting algorithm is shown to closely resemble the purely plastically anisotropic one once the appropriate eigenspace is identified. The proposed generalized radial-return algorithm is compared to a classical closest-point projection algorithm, for which it is shown to provide considerable advantage in computational cost. In conclusion, the efficiency, accuracy, and robustness of the algorithm are demonstrated through various illustrative test cases and in the finite element simulation of Taylor impact tests on tantalum.

- Authors:

- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Publication Date:

- Research Org.:
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1481138

- Alternate Identifier(s):
- OSTI ID: 1463918

- Report Number(s):
- LA-UR-17-30973

Journal ID: ISSN 0029-5981

- Grant/Contract Number:
- AC52-06NA25396

- Resource Type:
- Accepted Manuscript

- Journal Name:
- International Journal for Numerical Methods in Engineering

- Additional Journal Information:
- Journal Volume: 116; Journal Issue: 3; Journal ID: ISSN 0029-5981

- Publisher:
- Wiley

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING; 36 MATERIALS SCIENCE; algorithm efficiency; anisotropy; elastoplasticity; finite element method; return mapping; von Mises

### Citation Formats

```
Versino, Daniele, and Bennett, Kane C. Generalized radial-return mapping algorithm for anisotropic von Mises plasticity framed in material eigenspace. United States: N. p., 2018.
Web. doi:10.1002/nme.5921.
```

```
Versino, Daniele, & Bennett, Kane C. Generalized radial-return mapping algorithm for anisotropic von Mises plasticity framed in material eigenspace. United States. doi:10.1002/nme.5921.
```

```
Versino, Daniele, and Bennett, Kane C. Tue .
"Generalized radial-return mapping algorithm for anisotropic von Mises plasticity framed in material eigenspace". United States. doi:10.1002/nme.5921. https://www.osti.gov/servlets/purl/1481138.
```

```
@article{osti_1481138,
```

title = {Generalized radial-return mapping algorithm for anisotropic von Mises plasticity framed in material eigenspace},

author = {Versino, Daniele and Bennett, Kane C.},

abstractNote = {A computationally efficient integration algorithm for anisotropic plasticity is proposed, which is identified as a generalization of the radial-return mapping algorithm to anisotropy. The algorithm is based upon formulation within the eigenspace of a material anisotropy tensor associated with anisotropic quadratic von Mises (J2) plasticity (also called Hill plasticity), for which it is shown to ensure that the flow rule remains associative, ie, the normality condition is satisfied. Extension of the algorithm to include anisotropic elasticity (anisotropic elastoplasticity) is further provided, made possible by the identification of a certain fourth-order material tensor dependent on both the elastic and plastic anisotropy. The derivation of the fully elastoplastically anisotropic algorithm involves further complexity, but the resulting algorithm is shown to closely resemble the purely plastically anisotropic one once the appropriate eigenspace is identified. The proposed generalized radial-return algorithm is compared to a classical closest-point projection algorithm, for which it is shown to provide considerable advantage in computational cost. In conclusion, the efficiency, accuracy, and robustness of the algorithm are demonstrated through various illustrative test cases and in the finite element simulation of Taylor impact tests on tantalum.},

doi = {10.1002/nme.5921},

journal = {International Journal for Numerical Methods in Engineering},

number = 3,

volume = 116,

place = {United States},

year = {2018},

month = {7}

}

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