MOMAP

Lattice materials may induce a structural mass gain of magnitude 10 [Fleck, 2010]. However three scientific obstacles remain: - their fabrication cost - the computation of the optimal cell shape that remains long and difficult with the actual local methods [Laszczyk, 2011] - the quality control and the measurement of their mechanical properties which is quite impossible with classical mechanical testings [Bréchet, 2013] We will try to resolve the last two points. Topological optimisation is used to obtain the optimal shape of a bulk material. Here, given the global shape, we will search for the optimal local geometry of the cells (links widths, angles). The optimisation will be carried out by using the concept of homogeneous equivalent material concept, from its stiffness tensor, elastic and linearity limits and fabricability limits. The latter are associated to the 3D printing process of these materials. One participant [Olive, 2017] co-discovered the first set of stiffness tensor invariants. We will use some of these invariants and the orientation parameters within the optimisation process. The elasticity and the elasticity limits will be calculated analytically. In order to measure their actual value a testing device will be designed and realised. The boundary conditions will be imposed thanks to special links in order not to develop second gradient elasticity [Poncelet, 2018] and to obtain an homogenous strain field. In order to excite a sufficient number of strain states an hexapod (Stewart platform) device will be used. The strain filed will be measured thanks to 3D X-ray tomography. Tomography involves a reconstruction from a 3D volume from a collection of 2D radiographs. We will adapt the VIC (Virtual Image Correlation) method [Réthoré, 2013] for that. Using a parameteric description of the cells, it acts as an optimal filter, leading to better imaging resolution. This method will be used for the geometrical defects detection from tomographies at the cell scale. A coupled DIC (Digital Image Correlation) and VIC method will be developed and used at the structure scale for the specimen strain field measurement. CEA and Dorel company are partners of the projet. CEA will manufacture specimens and two structures of metallic lattices. These structures will be optimised thanks to the developed method and tested in order to verify their performances. Dorel will establish the specifications of a sketch structure (made of polymer) close to a baby equipment. One of them will be optimised with the new method and the other with present tools. They will be tested in order to estimate the gain of performance. Fleck, N.A., Deshpande, V.S., Ashby, M.F. (2010). Micro-architectured materials: past, present and future. Proceedings of the royal society of London A. Vol. 466, No. 2121, pp. 2495-2516. Laszczyk, L. (2011). Homogénéisation et optimisation topologique de panneaux architecturés, Thèse de Doctorat, Université de Grenoble. Olive, M., Kolev, B., Auffray, N. (2017). A minimal integrity basis for the elasticity tensor. Archive for Rational Mechanics and Analysis, 226(1), 1-31. Poncelet, M., Somera, A, Morel, C., Jailin, C, Auffray, N. (2019) An experimental evidence of the failure of Cauchy elasticity for the overall modeling of a non- centro-symmetric lattice under static loading. International Journal of Solids and Structures, 147 (15), 223-237 Réthoré, J. et François, M. (2013). Curve and boundaries measurement using B-splines and virtual images, Optics and Lasers in Engineering, 52, 145-155.