# Prediction of Short Fiber Composite Properties by an Artificial Neural Network Trained on an RVE Database

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## Abstract

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## 1. Introduction

^{2}Method [6], the required calculation time of complex technical components can be extreme. Within this method, an RVE is considered and solved with a finite element analysis (FEA) for each point of an FEA of a technical component.

^{2}Method could be overcome by neural networks. With neural networks, it is possible to approximate complex mathematical relations by very fast evaluable functions. Necessary for this is a sufficiently large amount of data about the relation, which will be approximated.

^{2}approach and the results will still be based on detailed RVEs requiring less assumptions compared to homogenization methods like the method of Mori–Tanaka.

## 2. Materials and Methods

## 3. Results and Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Illustration of four representative volume elements (RVEs) (each with 100 fibers) with different random parameters of the microstructure.

**Figure 3.**Correlation plot between all parameters of the RVE’s for two different input datasets. Dataset 1 features a constant Poisson’s ratio of the matrix material and Dataset 2 has a higher minimum fiber volume fraction.

**Figure 5.**Training behavior of the neural network for each training epoch. The neural network is evaluated by the objective function for the training data (Loss) and the validation data (Validation Loss).

**Figure 6.**Boxplot of minimum Validation Loss and mean training time per epoch for each architecture.

**Figure 7.**Comparison between Stiffness by RVE and Stiffness predictions by the neural network method (NN) and Mori–Tanaka Method (MT).

**Figure 9.**Direct comparison between model predictions of NN and MT for different input parameters. All input parameters are constant (see Table 2) except that one which is varied in the associated column.

Parameter | Dataset 1 | Dataset 2 |
---|---|---|

${E}_{M}$ | 500–2000 MPa | 500–2000 MPa |

$n{u}_{M}$ | 0.42 | 0.1–0.45 |

${a}_{R}$ | 1–20 | 1–20 |

${v}_{F}$ | 0.01–0.2 | 0.05–0.2 |

${a}_{ii}$ | 0–1 | 0–1 |

Parameter | Constant Value |
---|---|

${E}_{M}$ | 1500 MPa |

$n{u}_{M}$ | 0.42 |

${a}_{R}$ | 15 |

${v}_{F}$ | 0.15 |

${a}_{11}$ | 0.8, 0.5 and 0.33 |

${a}_{22}$ | 0.15, 0.5 and 0.33 |

${a}_{33}$ | 0.05, 0.0 and 0.33 |

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**MDPI and ACS Style**

Breuer, K.; Stommel, M.
Prediction of Short Fiber Composite Properties by an Artificial Neural Network Trained on an RVE Database. *Fibers* **2021**, *9*, 8.
https://doi.org/10.3390/fib9020008

**AMA Style**

Breuer K, Stommel M.
Prediction of Short Fiber Composite Properties by an Artificial Neural Network Trained on an RVE Database. *Fibers*. 2021; 9(2):8.
https://doi.org/10.3390/fib9020008

**Chicago/Turabian Style**

Breuer, Kevin, and Markus Stommel.
2021. "Prediction of Short Fiber Composite Properties by an Artificial Neural Network Trained on an RVE Database" *Fibers* 9, no. 2: 8.
https://doi.org/10.3390/fib9020008