Artificial Neural Network as a numerical formof effective constitutive law for composites with parametrized and hierarchical microstructure

Abstract

In the paper, Artificial Neural Network with hidden layers is used to approximate the functional dependence of the effective properties of a composite on the physical properties of its micro-components. Two numerical examples have been examined in order to demostrate this approach. The first one introduces geometrical parameters of the cell of periodicity into ANN training process. It proves the ability of ANN to catch the behaviour of the composite material based on the properties of the components and their spatial arrangement at micro level. The second example deals with a special case of the self-repetitive composite structure. It has been shown that, in the limit, the geometry and behaviour of such a composite is consistent with the fractal form known in the literature as the Sierpinski's carpet.