Architectured materials design by topology optimization with the level sets methods: influence of graded interfaces, fabrication constraints and (to come) optimum for in-use properties
One of the paradigm to fill the holes in materials maps is to develop « architectured materials ». This has been adresses since late 90s by O. Sigmund and coworkers  with the so-called SIMP method. In a collaboration with G. Allaire and co-workers from CMAP (Ecole Polytechnique), the topology description with level sets functions as this can account naturally for interface effects and multi-materials, first initiated during N. Vermaak post-doc (now at Lehigh university) , and further and deeper developed during A. Faure PhD  supported by the labeX CEMAM, in which G. Michailidis (now at ANSYS) and C. Dapogny (LJK, UGA) were involved. Heterogeneous materials with extreme thermo-elastic properties were designed  and later the questions of processing with account for fabrication constraints considered .
In the (near) future, we will focus in accounting for « usage properties » (fatigue, plasticity, failure, non linear effects) in the final design. This will be perform within a topology optimization platform developed by A. Faure during his PhD.
Design of thermo-elastic heterogeneous microstructures, with various local mechanisms (from ):
On the left, theoretical thermo-elastic bounds derived by [Gibianski & Torquato, 1997, JMPS], predictions with a sharp interface from [Sigmund 2000, JMPS] and comparison with graded interfaces . On the right, various design not best performant but providing insight on the operating mechanisms.
 BensØe M.P. , Sigmund O. , 2004, Topology optimization, Springer, 370P.
 Vermaak N., Michailidis G., Parry G. Estevez R., Allaire G. Bréchet Y., 2014, Material interface effects on the topology optimizationof multi-phase structures using a level set method, SMO, 50:623-644
 Faure A., PhD, Université de Grenoble Alpes, 2017, Optimisation de forme de matériaux et structures architecturés par la méthode des lignes de niveaux avec prise en compte des interfaces graduées
 Faure A., Michailidis G., Parry G., Vermaak N., Estevez R., 2017, Design of thermo-elastic multi-materials structures with graded interfaces using topology optimization, S.M.O., 56:823-837
 Allaire G., Dapogny C., EstevezR., Faure A., Michailidis G., 2017, Structural optimization under overhangs contraints imposed by additive manufacturing technologes,J Comp Phys, 351: 295-328