Abstract
The use of composite materials has increased lately and the need to know the behavior of these materials is very important once these devices are subject to suffer from damage such as cracks and delamination. Normally, to analyze failure problems in composite materials, the following steps are necessary: (1) structure geometry design, (2) numerical and/or experimental analysis and (3) use of failure criteria (e.g., Tsai–Wu failure criterion). If the used composite material has a non-expected failure criterion, the procedure must be repeated. In order to eliminate the procedure above, this study proposes the use of an artificial neural networks (ANN) inversion which can be used to determine an adequate configuration for the layers of the composite material from the desired failure criteria value. Numerical simulations, based on the finite element method, were made in order to create a database for ANN training and validation. After the inversion of the ANN, satisfactory results were obtained and this procedure could be used to minimize the high number of numerical simulations normally used in the design of a composite device.
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The authors would like to acknowledge the financial support from the Brazilian agency CAPES – Coordenação de Aperfeiçoamento de Pessoal de Nível Superior.
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Appendix
Appendix
In order to verify the correlation between the data used in the ANN training and validation, a linear regression analysis was proposed. In this study were considered independent variables that are known orientations and the dependent variables that are the orientation generated by the network. The fit is measured by coefficient of determination (R2), that has its values \(0 \le R^{2} \le 1\), nearer on one the coefficient demonstrates that the variables clarify the regression model [16].
Regression analysis was made for the neural network with three layers and an input, three layers and two inputs and six layers and one input (Fig. 6).
(a) Regression analysis of three layers, (b) regression analysis of three-layer neural network with two inputs, and (c) regression analysis of six layers
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Diniz, C.A., Cunha, S.S., Gomes, G.F. et al. Optimization of the Layers of Composite Materials from Neural Networks with Tsai–Wu Failure Criterion. J Fail. Anal. and Preven. 19, 709–715 (2019). https://doi.org/10.1007/s11668-019-00650-w
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DOI: https://doi.org/10.1007/s11668-019-00650-w