# A nonlocal, ordinary, state-based plasticity model for peridynamics.

## Abstract

An implicit time integration algorithm for a non-local, state-based, peridynamics plasticity model is developed. The flow rule was proposed in [3] without an integration strategy or yield criterion. This report addresses both of these issues and thus establishes the first ordinary, state-based peridynamics plasticity model. Integration of the flow rule follows along the lines of the classical theories of rate independent J{sub 2} plasticity. It uses elastic force state relations, an additive decomposition of the deformation state, an elastic force state domain, a flow rule, loading/un-loading conditions, and a consistency condition. Just as in local theories of plasticity (LTP), state variables are required. It is shown that the resulting constitutive model does not violate the 2nd law of thermodynamics. The report also develops a useful non-local yield criterion that depends upon the yield stress and horizon for the material. The modulus state for both the ordinary elastic material and aforementioned plasticity model is also developed and presented.

- Authors:

- Publication Date:

- Research Org.:
- Sandia National Laboratories

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1018475

- Report Number(s):
- SAND2011-3166

TRN: US201114%%157

- DOE Contract Number:
- AC04-94AL85000

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 36 MATERIALS SCIENCE; ADDITIVES; ALGORITHMS; DEFORMATION; PLASTICITY; THERMODYNAMICS

### Citation Formats

```
Mitchell, John Anthony.
```*A nonlocal, ordinary, state-based plasticity model for peridynamics.*. United States: N. p., 2011.
Web. doi:10.2172/1018475.

```
Mitchell, John Anthony.
```*A nonlocal, ordinary, state-based plasticity model for peridynamics.*. United States. doi:10.2172/1018475.

```
Mitchell, John Anthony. Sun .
"A nonlocal, ordinary, state-based plasticity model for peridynamics.". United States. doi:10.2172/1018475. https://www.osti.gov/servlets/purl/1018475.
```

```
@article{osti_1018475,
```

title = {A nonlocal, ordinary, state-based plasticity model for peridynamics.},

author = {Mitchell, John Anthony},

abstractNote = {An implicit time integration algorithm for a non-local, state-based, peridynamics plasticity model is developed. The flow rule was proposed in [3] without an integration strategy or yield criterion. This report addresses both of these issues and thus establishes the first ordinary, state-based peridynamics plasticity model. Integration of the flow rule follows along the lines of the classical theories of rate independent J{sub 2} plasticity. It uses elastic force state relations, an additive decomposition of the deformation state, an elastic force state domain, a flow rule, loading/un-loading conditions, and a consistency condition. Just as in local theories of plasticity (LTP), state variables are required. It is shown that the resulting constitutive model does not violate the 2nd law of thermodynamics. The report also develops a useful non-local yield criterion that depends upon the yield stress and horizon for the material. The modulus state for both the ordinary elastic material and aforementioned plasticity model is also developed and presented.},

doi = {10.2172/1018475},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2011},

month = {5}

}