INVERSE PROBLEMS IN THE LIGHT OF HOMOGENIZATION METHODS: IDENTIFICATION OF A COMPOSITE MICROSTRUCTURE

In this paper we explore the possibility of using machine learning techniques to identify the characteristics of the initial components of a composite, starting from the knowledge of the macrobehavior of the heterogeneous material or structure. For a periodic medium, we show that the inverse relation can be approximated as easily as the direct one. We focus on the use of artificial neural networks, which are trained with the macroscale properties at the input layer and with the microstructural parameters at the output layer. For the training process, the pairs of macroscale properties— microstructural parameters are obtained by solving a set of boundary value problems for the unit cell, by means of a numerical homogenization procedure. In recall mode, the trained network attributes to the measured or wanted macroproperties at the input the unknown or sought microstructural parameters at the output. The presented method proved computationally efficient and can be a valid alternative when the analytical formulation of the homogenization inverse problem results is very difficult.