Emeline Sadoulet-Reboul

Identification of representative anisotropic material properties accounting for friction and preloading effects: A contribution for the modeling of structural dynamics of electric motor stators:

Simulating the dynamic behavior and determining equivalent material properties for anisotropic models, superelements or structures subjected to preloads or friction remains a challenging issue. Amongst other practical applications, modeling interactions between the steel sheets in industrial magnetic cores of electric motor stators is a complex task, as it requires anticipating behavioral heterogeneities in the structure, and possibly represents significantly costly operations for performing modal or dynamic response simulations. In this article, a method for identifying equivalent material properties to anisotropic structures is developed, which is able to take into account the influence of preloads and friction on the material properties, later used in structural dynamics simulations. The proposed approach can be used with superelements, converting stiffness matrices into elasticity matrices. The method is first applied to a triclinic model, and recreates its elasticity matrix with little derivation. Then, an equivalent linear material is computed for a continuous structure under preloading. Compared at low frequencies, the vibration behavior of the preloaded structure and its equivalent effective media are in good agreement. The operation is repeated with a laminated stack under preloading. Again, the dynamic behavior of the equivalent structure shows good accuracy compared to the initial preloaded stack. Finally, the magnetic core of an electric machine stator is modeled with equivalent anisotropic material properties, accounting for friction and preload in the yokes and the teeths steel sheets. The simulation of the structures low-frequency radial vibration modes is satisfying, and shows improvement compared to orthotropic properties.

Design and experimental validation of an adaptive phononic crystal using highly dissipative polymeric material interface

In this paper, some numerical tools for dispersion analysis of periodic structures are presented, with a focus on the ability of the methods to deal with dissipative behaviour of the systems. An adaptive phononic crystal based on the combination of metallic parts and highly dissipative polymeric interface is designed. The system consists in an infinite periodic bidirectional waveguide. The periodic cylindrical pillars include a layer of shape memory polymer and Aluminum. The mechanical properties of the polymer depend on both temperature and frequency and can radically change from glassy to rubbery state, with various combination of high/low stiffness and high/low dissipation. A fractional derivative Zener model is used for the description of the frequency-dependent behaviour of the polymer. A 3D finite element model of the cell is developed for the design of the metamaterial. The ”Shifted-Cell Operator” technique consists in a reformulation of the PDE problem by ”shifting” in terms of wave number the space derivatives appearing in the mechanical behaviour operator inside the cell, while imposing continuity boundary conditions on the borders of the domain. Damping effects can easily be introduced in the system and a quadratic eigenvalue problem yields to the dispersion properties of the periodic structure. In order to validate the design and the adaptive character of the metamaterial, results issued from a full 3D model of a finite structure embedding an interface composed by a distributed set of the unit cells are presented. Various driving temperature are used to change the behaviour of the system. After this step, a comparison between the results obtained using the tunable structure simulation and the experimental results is presented. Two states are obtained by changing the temperature of the polymeric interface: at 25°C, the bandgap is visible around a selected frequency. Above the glass transition, the phononic crystal tends to behave as an homogeneous plate.

Parametric study of wave propagation in hierarchical auxetic perforated metamaterials

The understanding of wave propagation in a metamaterial with hierarchical, auxetic rectangular perforations is presented in this work. The metamaterial is a 2D structure with chaining horizontal and vertical perforations exhibiting auxetic in-plane behaviour. The unit cell of this lattice is identified as the reference level 0. Hierarchical structures are composed of structural elements which themselves have structure. At level 0, 4 rigid squares are present in the unit cell. In each square, the reference structure is used by applying a scale ratio to obtain the level 1. The same strategy is used to reach the upper level in each subunit. A geometric parametric investigation of these rectangular perforations using a numerical asymptotic homogenisation finite element approach is done. Some numerical eigenvalue tools are used for the dispersion analysis of this structure. It is first observed that the total width of Band gaps increases with the hierarchy. The porosity induced by the perforations is taken into account in the mechanical properties. The symmetry of the geometry in the x-y plane allow to define the entire geometry of the unit cell using only 2 parameters: the void aspect ratio, the intercell spacing and the hierarchy level. When decreasing the intercell spacing, the total width of Band gaps increases and the effective stiffness in x and y directions decrease, allowing for increased rotations of the rigid squares, so auxetic behaviour is greater. Hierarchical levels shift from isotropic to orthotropic, hierarchical levels are always auxetic.