# Prediction of Composite Mechanical Properties: Integration of Deep Neural Network Methods and Finite Element Analysis

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Simulation-Based Datasets

#### 2.2. Machine Learning Approach

## 3. Results

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Overall framework that bridged FE analysis with DNN networks to predict the Young’s modulus and Poisson’s ratio of BGs-COL.

**Figure 2.**Three patterns of BGs embedded in the COL: (

**a**) circular BGs shapes with the same diameter as a uniform dataset; (

**b**) BGs distributed in the COL with circular shapes and different diameters as a non-uniform dataset; (

**c**) free-shape BGs embedded in the COL as an irregular dataset.

**Figure 3.**Performance of the ResNet model in extracting the elastic property of the composite hydrogel including the Young’s modulus (E11) and Poisson’s ratio (ν12) on the (

**a**,

**d**) uniform dataset, (

**b**,

**e**) non-uniform dataset, (

**c**,

**f**) irregular dataset, and (

**g**,

**h**) full dataset. (

**i**) Comparison of the ReLU and Leaky ReLU activation function performance in terms of MAE for ResNet and AlexNet on the full dataset.

**Figure 4.**Performance of the AlexNet model in extracting the elastic property of the composite hydrogel including the Young’s modulus (E11) and Poisson’s ratio (ν12) on the (

**a**,

**d**) uniform dataset, (

**b**,

**e**) non-uniform dataset, (

**c**,

**f**) irregular dataset, and (

**g**,

**h**) full dataset.

**Table 1.**Using AlexNet and ResNet, we evaluated the performance of our implemented ResNet and AlexNet networks with an 85:15 train–test split. The performances were measured according to the error between the FEM results and the predicted Young’s modulus and Poisson’s ratio derived from the trained AlexNet and ResNet. Statistical descriptors are provided for context (MAE, MSE, R-value, and average of distributed data using the max–min normalization method).

Network | Dataset | Properties | MAE | MSE | R^{2} | Average |
---|---|---|---|---|---|---|

AlexNet | Uniform | E11 | 0.032 | 0.001 | 0.99 | 0.373 |

ν12 | 0.053 | 0.004 | 0.98 | 0.587 | ||

Non-uniform | E11 | 0.011 | 0.001 | 0.99 | 0.382 | |

ν12 | 0.143 | 0.026 | 0.95 | 0.591 | ||

Irregular | E11 | 0.013 | 0.001 | 0.99 | 0.491 | |

ν12 | 0.068 | 0.006 | 0.92 | 0.561 | ||

Full | E11 | 0.044 | 0.003 | 0.99 | 0.258 | |

ν12 | 0.023 | 0.001 | 0.97 | 0.716 | ||

ResNet | Uniform | E11 | 0.053 | 0.005 | 0.97 | 0.373 |

ν12 | 0.062 | 0.007 | 0.94 | 0.587 | ||

Non-uniform | E11 | 0.056 | 0.005 | 0.98 | 0.382 | |

ν12 | 0.046 | 0.003 | 0.95 | 0.591 | ||

Irregular | E11 | 0.045 | 0.003 | 0.96 | 0.491 | |

ν12 | 0.077 | 0.008 | 0.85 | 0.561 | ||

Full | E11 | 0.079 | 0.008 | 0.97 | 0.258 | |

ν12 | 0.074 | 0.007 | 0.96 | 0.716 |

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**MDPI and ACS Style**

Gholami, K.; Ege, F.; Barzegar, R. Prediction of Composite Mechanical Properties: Integration of Deep Neural Network Methods and Finite Element Analysis. *J. Compos. Sci.* **2023**, *7*, 54.
https://doi.org/10.3390/jcs7020054

**AMA Style**

Gholami K, Ege F, Barzegar R. Prediction of Composite Mechanical Properties: Integration of Deep Neural Network Methods and Finite Element Analysis. *Journal of Composites Science*. 2023; 7(2):54.
https://doi.org/10.3390/jcs7020054

**Chicago/Turabian Style**

Gholami, Kimia, Faraz Ege, and Ramin Barzegar. 2023. "Prediction of Composite Mechanical Properties: Integration of Deep Neural Network Methods and Finite Element Analysis" *Journal of Composites Science* 7, no. 2: 54.
https://doi.org/10.3390/jcs7020054