# An evolving effective stress approach to anisotropic distortional hardening

## Abstract

A new yield surface with an evolving effective stress definition is proposed for consistently and efficiently describing anisotropic distortional hardening. Specifically, a new internal state variable is introduced to capture the thermodynamic evolution between different effective stress definitions. The corresponding yield surface and evolution equations of the internal variables are derived from thermodynamic considerations enabling satisfaction of the second law. A closest point projection return mapping algorithm for the proposed model is formulated and implemented for use in finite element analyses. Finally, select constitutive and larger scale boundary value problems are solved to explore the capabilities of the model and examine the impact of distortional hardening on constitutive and structural responses. Importantly, these simulations demonstrate the tractability of the proposed formulation in investigating large-scale problems of interest.

- Authors:

- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Solid Mechanics Dept.

- Publication Date:

- Research Org.:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

- Sponsoring Org.:
- USDOE National Nuclear Security Administration (NNSA)

- OSTI Identifier:
- 1431215

- Alternate Identifier(s):
- OSTI ID: 1582877

- Report Number(s):
- SAND-2018-2639J

Journal ID: ISSN 0020-7683; 661559

- Grant/Contract Number:
- AC04-94AL85000; NA0003525

- Resource Type:
- Accepted Manuscript

- Journal Name:
- International Journal of Solids and Structures

- Additional Journal Information:
- Journal Volume: 143; Journal ID: ISSN 0020-7683

- Publisher:
- Elsevier

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 42 ENGINEERING; Anisotropic hardening; Distortional hardening; Yield surface; Return mapping algorithm; Plasticity

### Citation Formats

```
Lester, B. T., and Scherzinger, W. M. An evolving effective stress approach to anisotropic distortional hardening. United States: N. p., 2018.
Web. doi:10.1016/j.ijsolstr.2018.03.007.
```

```
Lester, B. T., & Scherzinger, W. M. An evolving effective stress approach to anisotropic distortional hardening. United States. doi:10.1016/j.ijsolstr.2018.03.007.
```

```
Lester, B. T., and Scherzinger, W. M. Sun .
"An evolving effective stress approach to anisotropic distortional hardening". United States. doi:10.1016/j.ijsolstr.2018.03.007. https://www.osti.gov/servlets/purl/1431215.
```

```
@article{osti_1431215,
```

title = {An evolving effective stress approach to anisotropic distortional hardening},

author = {Lester, B. T. and Scherzinger, W. M.},

abstractNote = {A new yield surface with an evolving effective stress definition is proposed for consistently and efficiently describing anisotropic distortional hardening. Specifically, a new internal state variable is introduced to capture the thermodynamic evolution between different effective stress definitions. The corresponding yield surface and evolution equations of the internal variables are derived from thermodynamic considerations enabling satisfaction of the second law. A closest point projection return mapping algorithm for the proposed model is formulated and implemented for use in finite element analyses. Finally, select constitutive and larger scale boundary value problems are solved to explore the capabilities of the model and examine the impact of distortional hardening on constitutive and structural responses. Importantly, these simulations demonstrate the tractability of the proposed formulation in investigating large-scale problems of interest.},

doi = {10.1016/j.ijsolstr.2018.03.007},

journal = {International Journal of Solids and Structures},

number = ,

volume = 143,

place = {United States},

year = {2018},

month = {3}

}

#### Figures / Tables:

Figures / Tables found in this record:

*Figures/Tables have been extracted from DOE-funded journal article accepted manuscripts.*