Multiscale approach for the thermomechanical analysis of hierarchical structures

In this chapter we briefly review the most common methods to obtain equivalent properties and then consider full multiscale modelling. Both linear and non-linear material behaviours are considered. The case of composites with periodic microstructure is dealt with in detail and an example shows the capability of the method. Particular importance is also given to nonconventional methods which make use of Artificial Neural Networks (ANN). It is shown how ANN can be used either to substitute the overall material relationship (ANN routines can be easily incorporated in a Finite Element code) or to identify the parameters of the constitutive relation between averages (i.e. relating volume-averaged field variables).