Abstract
Design of new materials is quite a difficult task owing to various time and length scales and affiliated uncertainties. The major challenge is to include all these in a conventional model. Hyperparameter models in machine learning can be used to overcome these issues. In this paper, an artificial neural network (ANN) model is developed to estimate the effective elastic parameters of unidirectional fiber reinforced composites using representative volume elements (RVE) considering uncertainty in the fiber diameter. The diameter probability distribution is constructed from the acquired gray images by employing image processing operations. The generalized Polynomial Chaos (gPC) expansion is then used to represent the distribution as a random input parameter for finite element analysis, from where the effective parameters are realized. Similarly, the outputs of the FE model, i.e., elastic parameters, are approximated by gPC expansions having unknown deterministic coefficients and random orthogonal Hermite polynomials. A set of collocation points are generated from roots of the random polynomials; from there, the unknown coefficients are estimated. The realization samples are utilized to train an ANN algorithm based on supervised deep learning. The developed ANN model is later tested and validated for a new sample set of data. It is shown that the ANN model with few hidden layers and neurons has a high accuracy for estimation of the elastic parameters directly from the information on the distribution of fiber diameters.
Highlights
Under many situations, the conventional modeling and simulations for calculation of state parameters break down due to material being nonlinear, multiscale, unknown, and high dimensional, as well as uncertainty, etc
artificial neural network (ANN) model with few hidden layers and neurons has a high accuracy for estimation of the elastic parameters directly from the information on the distribution of fiber diameters
A deep learning ANN model has been developed for prediction of the elastic parameters of the UD fiber lamina using representative volume elements (RVE) cells from the given probability distribution of the random fiber diameter
Summary
The conventional modeling and simulations for calculation of state parameters break down due to material being nonlinear, multiscale, unknown, and high dimensional, as well as uncertainty, etc. The estimation of such parameters for the heterogeneous materials based on multiscale micromechanics models have been widely explored in past decades [1], analytically and numerically [2,3,4,5]. It is mandatory to include the details of each scale, including uncertainties between scales Involving all these in a physics-based conventional modeling tool such as the FE method is not possible, or at least very difficult for implementation.
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