# Verification and Validation of a Three-Dimensional Orthotropic Plasticity Constitutive Model Using a Unidirectional Composite

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## Abstract

**:**

## 1. Introduction

## 2. Theoretical Details

#### 2.1. Non-Associated Plastic Flow

#### 2.2. Flow Rule and Determination of Flow Rule Coefficients

#### 2.3. Modeling Damage

## 3. Experimental and Numerical Modeling Studies

## 4. Discussion

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 2.**Side view (Optical Microscopy). 1: Longitudinal (fiber) direction; 3: Through-thickness direction.

**Figure 4.**Details of impact test: (

**a**) Small impact gun; (

**b**) Inside view of test chamber; (

**c**) Photograph showing the hollow projectile; (

**d**) Drawing of 30.48 cm × 30.48 cm (12 in × 12 in) panel with a 25.4 cm (10 in) dia circular clamping pattern and support plate; (

**e**) Close up photograph of test article (before impact); (

**f**) Close up photograph showing the back face of the speckled test article (after impact).

**Figure 5.**LS-DYNA finite element model: (

**a**) View of back panel; (

**b**) Side view; (

**c**) View showing projectile just before impacting the panel.

**Figure 6.**Contour plots of the out-of-plane (Z) displacement at time t = 0.0007 s. (

**a**) Experiment; (

**b**) MAT213 FE model; (

**c**) MAT22 FE model.

**Figure 7.**Maximum out-of-plane (Z) displacement versus time plot for the impact test (LVG905), MAT213 and MAT22 simulations.

**Figure 8.**Graph of kinetic energy, internal energy and hourglass energy (MAT213 model) as a function of time.

Model Parameter | Value |
---|---|

Mass density (g/mm^{3}) | 1.55 (10^{−3}) |

E_{a} (GPa) | 1.51 (10^{2}) |

E_{b} (GPa) | 7.89 |

E_{c} (GPa) | 7.89 |

ν_{ba} | 0.01385 |

ν_{bc} | 0.01385 |

ν_{ca} | 0.3792 |

G_{ab} (GPa) | 4.00 |

G_{bc} (GPa) | 2.24 |

G_{ca} (GPa) | 4.00 |

Shear Strength (MPa) | 94.87 |

Longitudinal Tensile Strength (GPa) | 2.84 |

Transverse Tensile Strength (GPa) | 0.060 |

Transverse Compressive Strength (GPa) | 0.168 |

Alpha | 0.0 |

Normal Tensile Strength (MPa) | 60.12 |

Transverse Shear Strength (MPa) | 1.03 (10^{2}) |

Transverse Shear Strength (MPa) | 94.87 |

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## Share and Cite

**MDPI and ACS Style**

Hoffarth, C.; Khaled, B.; Shyamsunder, L.; Rajan, S.; Goldberg, R.; Carney, K.S.; DuBois, P.; Blankenhorn, G.
Verification and Validation of a Three-Dimensional Orthotropic Plasticity Constitutive Model Using a Unidirectional Composite. *Fibers* **2017**, *5*, 12.
https://doi.org/10.3390/fib5010012

**AMA Style**

Hoffarth C, Khaled B, Shyamsunder L, Rajan S, Goldberg R, Carney KS, DuBois P, Blankenhorn G.
Verification and Validation of a Three-Dimensional Orthotropic Plasticity Constitutive Model Using a Unidirectional Composite. *Fibers*. 2017; 5(1):12.
https://doi.org/10.3390/fib5010012

**Chicago/Turabian Style**

Hoffarth, Canio, Bilal Khaled, Loukham Shyamsunder, Subramaniam Rajan, Robert Goldberg, Kelly S. Carney, Paul DuBois, and Gunther Blankenhorn.
2017. "Verification and Validation of a Three-Dimensional Orthotropic Plasticity Constitutive Model Using a Unidirectional Composite" *Fibers* 5, no. 1: 12.
https://doi.org/10.3390/fib5010012