Artificial Neural Networks in Numerical Homogenization and Local Stress – Strain Recovery

In this paper we show some different concepts for the use of Artificial Neural Networks in modeling of composites and hierarchical structures. Starting from a relatively small set of suitable numerical experiments performed on a unit cell, a proper set of corresponding input-output data is created to train the network to identify the effective properties. Furthermore, ANN based procedures can be exploited in a multiscale analysis as a tool for the stress-strain recovery at lower levels of the hierarchical structure and/or to estimate the state of yielding of the materials. This kind of application is of great computational importance, since with material non linearity they allow for a significantly improved computational efficiency. Finally ANNs may be used to define the homogenized properties for a class of parameterized unit cells or when material characteristics depend upon a parameter (e.g. temperature, damage etc.). The problem of the best ANN (or sufficiently good ANN) for each type of applications is discussed by means of the examples presented.