# An Approach to Stochastic Peridynamic Theory

## Abstract

In many material systems, man-made or natural, we have an incomplete knowledge of geometric or material properties, which leads to uncertainty in predicting their performance under dynamic loading. Given the uncertainty and a high degree of spatial variability in properties of materials subjected to impact, a stochastic theory of continuum mechanics would be useful for modeling dynamic response of such systems. Peridynamic theory is such a theory. It is formulated as an integro- differential equation that does not employ spatial derivatives, and provides for a consistent formulation of both deformation and failure of materials. We discuss an approach to stochastic peridynamic theory and illustrate the formulation with examples of impact loading of geological materials with uncorrelated or correlated material properties. We examine wave propagation and damage to the material. The most salient feature is the absence of spallation, referred to as disorder toughness, which generalizes similar results from earlier quasi-static damage mechanics. Acknowledgements This research was made possible by the support from DTRA grant HDTRA1-08-10-BRCWM. I thank Dr. Martin Ostoja-Starzewski for introducing me to the mechanics of random materials and collaborating with me throughout and after this DTRA project.

- Authors:

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

- Publication Date:

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

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

- OSTI Identifier:
- 1432756

- Report Number(s):
- SAND-2018-3498

662032

- DOE Contract Number:
- AC04-94AL85000

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

### Citation Formats

```
Demmie, Paul N.
```*An Approach to Stochastic Peridynamic Theory*. United States: N. p., 2018.
Web. doi:10.2172/1432756.

```
Demmie, Paul N.
```*An Approach to Stochastic Peridynamic Theory*. United States. doi:10.2172/1432756.

```
Demmie, Paul N. Sun .
"An Approach to Stochastic Peridynamic Theory". United States.
doi:10.2172/1432756. https://www.osti.gov/servlets/purl/1432756.
```

```
@article{osti_1432756,
```

title = {An Approach to Stochastic Peridynamic Theory},

author = {Demmie, Paul N.},

abstractNote = {In many material systems, man-made or natural, we have an incomplete knowledge of geometric or material properties, which leads to uncertainty in predicting their performance under dynamic loading. Given the uncertainty and a high degree of spatial variability in properties of materials subjected to impact, a stochastic theory of continuum mechanics would be useful for modeling dynamic response of such systems. Peridynamic theory is such a theory. It is formulated as an integro- differential equation that does not employ spatial derivatives, and provides for a consistent formulation of both deformation and failure of materials. We discuss an approach to stochastic peridynamic theory and illustrate the formulation with examples of impact loading of geological materials with uncorrelated or correlated material properties. We examine wave propagation and damage to the material. The most salient feature is the absence of spallation, referred to as disorder toughness, which generalizes similar results from earlier quasi-static damage mechanics. Acknowledgements This research was made possible by the support from DTRA grant HDTRA1-08-10-BRCWM. I thank Dr. Martin Ostoja-Starzewski for introducing me to the mechanics of random materials and collaborating with me throughout and after this DTRA project.},

doi = {10.2172/1432756},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Sun Apr 01 00:00:00 EDT 2018},

month = {Sun Apr 01 00:00:00 EDT 2018}

}