Finite-element models of heterogeneous structures often need to be simplified by the means of representative equivalent homogeneous materials in order to simulate their mechanical behaviours with a reasonably low number of degrees of freedom. Some homogenization techniques already enable to create equivalent homogeneous materials to reliably represent 2D, laminated, honeycomb or various other composite structures. Fewer mature methods have been developed to analyse the behaviours of 3D heterogeneous structures. Also, the case of materials more complicated than orthotropic (e.g. anisotropic or triclinic) is hardly ever discussed in the literature, especially in dynamic applications to finite-element models. As for studies involving superelements or structures subjected to preloads or, there yet exists to the authors' knowledge no techniques able to identify equivalent material properties.

In this paper, a novel method of 3D-equivalent material identification is proposed for finite element anisotropic structures and for models subjected to preloads and friction. The method consists of several sets of finite-element simulations on representative models and enables computing the terms of equivalent materials' elasticity matrices rapidly and with low resource requirements. Its ability to identify shear-related coefficients differently according to sliding or transverse shear scenarios makes it adapted to laminated stacks as well as other types of heterogeneous periodic structures (such as particle-based composites). Unlike existing reference homogenization techniques, the influence of preloads or contact conditions such as friction can be taken into account in the identification of the equivalent elasticity matrix's 21 coefficients. In addition to this, the method may be applied to superelements in addition to fully-defined finite-element models, therefore presenting the possibility of conversion from stiffness to elasticity matrices.

First, a finite-element model of a preloaded 3D stratified structure is created, as well as its homogeneous, unloaded equivalent (of identical geometry). A representative elasticity matrix is computed for the laminated structure with the aid of this new method, and takes into account the influence of the preloads on the structure's global elastic behaviour. The first modes of the two finite element models are compared, showing that the equivalent material represents the stratified structure's dynamic behaviour with good accuracy.

Then, a finite-element model is created for the magnetic core of an electric motor stator. Consisting of several thousands of steel sheets individually coated with epoxy resin, the magnetic core is held in one piece by weld beads on its lateral face, inducing important heterogeneities in the behaviour of the entire structure. The finite-element model is therefore divided into several zones according to the distance to the weld beads. Taking into account friction properties as well as compression preloads resulting from the manufacturing process, specific elastic properties are computed and applied to each of the zones. Then, the first ovalization modes simulated with this finite-element model are compared to experimental data measured on a real stator, and show good agreement.

These results offer interesting perspectives for dynamic simulations of heterogeneous structures such as industrial electric machines, for which predicting the acoustic behaviours is a key issue for the automotive industry.