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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 [1] 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) [2], and further and deeper developed during A. Faure PhD [3] 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 [4] and later the questions of processing with account for fabrication constraints considered [5].
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 [4]):
FM7 figure 1 FM7 figure 2
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 [4]. On the right, various design not best performant but providing insight on the operating mechanisms.


[1] BensØe M.P. , Sigmund O. , 2004, Topology optimization, Springer, 370P.
[2] 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
[3] 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
[4] 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
[5] 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


Contact : Rafaël Estevez

Date of update March 12, 2020

Université Grenoble Alpes