A combined Finite Element - Artificial Neural Network approach for multiscale modeling of hierarchical structures

In this paper we present a combined finite element (FE) – artificial neural network (ANN) approach for the multi-scale modeling of cables made of LTS materials. At first different aspects of ANN use in non-linear analysis of hierarchical composite are shown. The possibility to model via ANNs the *homogenized material behavior* starting from a relatively small set of suitable virtual or real experiments is discussed. ANN based procedures can also be exploited in a multi-scale analysis as a tool for the *stress-strain recovery* at the structure lower levels. For example, in SC cables a map of the strain state at the wire and filament scale is needed. The related unsmearing procedure is numerically very costly. An ANN, acting in recall mode during the execution of the homogenization loops, allows for a considerably improved computational efficiency. Secondly, the *cable mechanical behavior* is analyzed, namely the influence of the hierarchical helix geometry on the stiffness of the cable. It is proven how the stiffness matrix of these structures is different from the usual matrix of Euler-Bernoulli beams. Finally, a significant application for the *design of cables* is shown. ANNs can be used to investigate the dependence of the stiffness coefficients upon the twist pitches of the multi-level helixes. The final goal of this research is to substitute, at each level, a bundle of wires with a single equivalent wire, having the characteristics computed on the bundle of the previous scale. The presented hybrid finite element–artificial neural network approach is exploited to this aim, showing that suitably trained ANNs can replace the module that usually provides the stiffness matrix in an FE code. In the end, some real cable examples are shown, where results obtained via the FE method are compared with those calculated by an ANN-FE procedure.