Multiscale numerical modeling of composite material: A combined FE-ANN approach

In this paper we present a combined finite element (FE) - artificial neural network (ANN) approach for the analysis of the behavior of non linear composites and hierarchical structures. Different aspects of ANN use in multiscale numerical homogenization are shown. First, the possibility to model via ANNs the effective material starting from a relatively small set of suitable virtual or real experiments performed on a unit cell is discussed. ANN based procedures can also be exploited in a multiscale analysis as a tool for the stress-strain recovery at lower levels of a hierarchical structure. In many situations a map of the strain and stress state at the lowest level is needed. To this aim, it is necessary to calculate the strain state in the most strained point for each material of the repetitive cell. In other cases, it is of interest to know if and when at least one of the non linear composite material is e.g. yielding, checking all the gauss points of all the elements. These two post-processing procedures, together with the unsmearing itself, are numerically very costly. An ANN, acting in recall mode during the execution of the homogenization loops, allows for a considerably improved computational efficiency. Finally, a significant application for the design of composites is shown. ANN can be used for the identification of the effective material coefficients of a system characterized by a cell of periodicity with a variable geometry.