Joint Finite Element - Artificial Neural Network Numerical Analysis of Multilevel Composites

In this paper we describe how an Artificial Neural Network (ANN) can be used to approximate and memorise parameters characterising an effective behaviour of hierarchical composites. The present approach uses directly results of the homogenisation theory. The asymptotic theory of homogenization permits to deduce the matrix of effective material characteristics for composite from given properties of components and their spatial arrangement inside the representative volume of the heterogeneous material (cell of periodicity). To compute the effective material properties, the applied version of the homogenisation technique needs a solution of a boundary value problem (BVP) with periodic boundary condition posed over the cell of periodicity. The effective material properties are computed point-wise for given data, i.e. for each new geometry of the cell and each variation of values of the properties of components. It is impossible to obtain a closed form expression for them. In our approach, neural network is used as an approximator of the functional dependence of components of the effective constitutive matrix on the micro-structural data. Independent variables are here the mechanical properties of the components and some parameters introduced to describe their geometrical repartition in the cell. The approximation, defined by computed examples, substitutes the closed form expression. ANN, used as a “functional formula”, replaces the solution of the BVP thus allows us to spare the time of computations when we deal with a multilevel composite.