# Simulation of dynamic fracture using peridynamics, finite element modeling, and contact.

## Abstract

Peridynamics is a nonlocal extension of classical solid mechanics that allows for the modeling of bodies in which discontinuities occur spontaneously. Because the peridynamic expression for the balance of linear momentum does not contain spatial derivatives and is instead based on an integral equation, it is well suited for modeling phenomena involving spatial discontinuities such as crack formation and fracture. In this study, both peridynamics and classical finite element analysis are applied to simulate material response under dynamic blast loading conditions. A combined approach is utilized in which the portion of the simulation modeled with peridynamics interacts with the finite element portion of the model via a contact algorithm. The peridynamic portion of the analysis utilizes an elastic-plastic constitutive model with linear hardening. The peridynamic interface to the constitutive model is based on the calculation of an approximate deformation gradient, requiring the suppression of possible zero-energy modes. The classical finite element portion of the model utilizes a Johnson-Cook constitutive model. Simulation results are validated by direct comparison to expanding tube experiments. The coupled modeling approach successfully captures material response at the surface of the tube and the emerging fracture pattern. The coupling of peridynamics and finite element analysis via amore »

- Authors:

- Publication Date:

- Research Org.:
- Sandia National Laboratories

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 1030270

- Report Number(s):
- SAND2010-7867C

TRN: US201124%%67

- DOE Contract Number:
- AC04-94AL85000

- Resource Type:
- Conference

- Resource Relation:
- Conference: Proposed for presentation at the ASME International Mechanical Engineering Congress and Exposition held November 12-18, 2010 in Vancouver, BC, Canada.

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 36 MATERIALS SCIENCE; ALGORITHMS; DEFORMATION; DISTRIBUTION; FRACTURES; FRAGMENTATION; HARDENING; HYDRODYNAMICS; INTEGRAL EQUATIONS; LINEAR MOMENTUM; MECHANICAL ENGINEERING; REMOVAL; SIMULATION; STEELS; VELOCITY

### Citation Formats

```
Littlewood, David John.
```*Simulation of dynamic fracture using peridynamics, finite element modeling, and contact.*. United States: N. p., 2010.
Web.

```
Littlewood, David John.
```*Simulation of dynamic fracture using peridynamics, finite element modeling, and contact.*. United States.

```
Littlewood, David John. Mon .
"Simulation of dynamic fracture using peridynamics, finite element modeling, and contact.". United States.
```

```
@article{osti_1030270,
```

title = {Simulation of dynamic fracture using peridynamics, finite element modeling, and contact.},

author = {Littlewood, David John},

abstractNote = {Peridynamics is a nonlocal extension of classical solid mechanics that allows for the modeling of bodies in which discontinuities occur spontaneously. Because the peridynamic expression for the balance of linear momentum does not contain spatial derivatives and is instead based on an integral equation, it is well suited for modeling phenomena involving spatial discontinuities such as crack formation and fracture. In this study, both peridynamics and classical finite element analysis are applied to simulate material response under dynamic blast loading conditions. A combined approach is utilized in which the portion of the simulation modeled with peridynamics interacts with the finite element portion of the model via a contact algorithm. The peridynamic portion of the analysis utilizes an elastic-plastic constitutive model with linear hardening. The peridynamic interface to the constitutive model is based on the calculation of an approximate deformation gradient, requiring the suppression of possible zero-energy modes. The classical finite element portion of the model utilizes a Johnson-Cook constitutive model. Simulation results are validated by direct comparison to expanding tube experiments. The coupled modeling approach successfully captures material response at the surface of the tube and the emerging fracture pattern. The coupling of peridynamics and finite element analysis via a contact algorithm has been shown to be a viable means for simulating material fracture in a high-velocity impact experiment. A combined peridynamics/finite element approach was applied to model an expanding tube experiment performed by Vogler, et al., in which loading on the tube is a result of Lexan slugs impacting inside the tube. The Lexan portion of the simulation was modeled with finite elements and a Johnson-Cook elastic-plastic material model in conjunction with an equation-of-state law. The steel tube portion of the simulation was modeled with peridynamics, an elastic-plastic material model, and a critical stretch bond damage model. The application of peridynamics to the tube portion of the model allowed the capture of the formation of cracks and eventual fragmentation of the tube. The simulation results yielded good agreement with the experimental results published by Vogler, et al., for the velocity and displacement profiles on the surface of the tube and the resulting fragment distribution. Numerical difficulties were encountered that required removal of hexahedron elements from the Lexan portion of the model over the course of the simulation. The significant number of inverted and nearly-inverted elements appearing over the course of the simulation is believed to be a result of irregularities in the contact between the Lexan and AerMet portions of the model, and was likely exacerbated by the ultra-high strength of the AerMet tube. Future simulations are planned in which the Lexan portion of the simulation is modeled with peridynamics, or with an alternative method such as smoothed particle hydrodynamics, with the goal of reducing these numerical difficulties.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2010},

month = {11}

}