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Projet ANR MAX-OASIS

**MAX-OASIS**

Matériaux Architecturés eXotiques, Ondes, AniSotropie, InStabilités

ANR-19-CE08-0005

Partenaires :

- MSME (UGE) resp. N. Auffray (porteur) ;

- PIMM (CNAM-ENSAM) resp. J. Dirrenberger ;

- LMT (ENS Cachan) resp. M. Poncelet ;

- d’Alembert (Sorbonne Université) resp. B. Desmorat.

Budget : 580k€

Période : 2019-2024

Résumé :

The current craze for architectured materials results from 3 factors:

1. Expected exceptional properties: Studies (experimental, numerical, theoretical) show that in addition to mass gain, the presence of an internal architecture significantly improves certain properties (energy absorption), or even creates others (invisibility cloak);

2. Shape optimization: Mesostructure design algorithms have emerged that allow a more automatic exploration of the links between architecture and resulting properties;

3. Additive manufacturing: Manufacturing techniques and their rapid development now make it possible to produce structures with complex internal architectures.

However, the expected exceptional properties occur when the scale of mechanical loading is close to that of the mesostructure. Wave propagation and instabilities are situations where the lack of scale separation is necessary for producing non-standard effects.

A streamlined approach to the design of such materials involves an intermediate step in which an equivalent effective medium is substituted to the mesostructure of the material. This effective continuum is first optimized, in order to satisfy a given set of specifications, then deshomogenized to reveal the desired mesostructure.

However, the classical framework of homogenization assumes infinite scale separation and is therefore ill-suited to continuous modelling of expected phenomena. Taking into account the effects of the mesostructure within a continuous modeling is the scientific lock this project proposes to remove. The developed approach is based on generalized continuum mechanics supplemented by the use of group theory in order to clarify the role of material symmetries on effective behavior. The framework concerns periodic and pseudo-periodic materials and the considered applications are, on the one hand, **control of wave propagation** (Axis 1) and, on the other hand, **prediction and control of instabilities** (Axis 2). In both cases, the architecture of the elementary cell is decisive. Its determination from the target effective properties via **an inverse problem of architecture** is at the core of Axis 3 of the project. These axes are complemented by a transversal axis linked to the development of adapted experimental methods. In more details:

1. **Elastodynamics of architectured materials:** Dynamics adds distribution of inertia to the optimization problem that traditionally only deals with distribution of stiffness. Depending on the applications, the various networks may or may not be congruent.

Fig.1 : The wave propagation in a honeycomb material. (top) standard honeycomb (bottom) optimized honeycomb for wave deviation. Courtesy of N. Auffray and G. Rosi at MSME

2. **Controlled instabilities**, obtained by a succession of stable post-bifurcated configurations. This requires an optimization of the crystallographic symmetries of the architectured materials. The applications here concern the adjustment of the multifunctional properties of materials by a change in mesostructure due to instabilities generated by a mechanical loading.

Fig.2 : Successive controlled instabilities in a grid-like material by C. Coulais

3. The definition of an **inverse problem of architecture** allowing to determine associated mesostructures, for a set of invariants of the given effective material. This axis aims both at "dehomogenizing" the results obtained in Axes 1 and 2 in order to obtain a real architecture, but also at exploring and classifying mesostructures associated with exotic elastic anisotropies (2D and 3D).

4. **Development of experimental methods** adapted to architectured materials. Experimental homogenization implies a specific control of boundary conditions. Moreover, instabilities will generate large displacements at the edges requiring the development of appropriate experimental means. This axis will be limited to the static behavior of architectured materials.

Fig.3 : Experimental setup for applying Kinematic Uniform Boundary Conditions developed at LMT by M. Poncelet