Mathematical modeling of the nonlinear mechanical response of graphene monolayers Dimitris Sfyris ([email protected]) Institute of Chemical Engineering Sciences Foundation for Research and Technology Patras, Greece

Graphene monolayers can go up to 20 per cent in tension in an elastic manner, therefore there is the need for a geometrically and materially nonlinear theory that describe such a response. Starting from the symmetries of graphene viewed as a multilattice, we lay down the full list of invariants that capture all nonlinear eects that graphene supports. We give some simple closed form solutions corresponding to simple loading histories and study stability against three dierent stability criteria. We also discuss the case when symmetry of graphene breaks.

Short Bio Dimitris Sfyris studied Mathematics at the University of Ioannina, Greece and received his PhD from the Civil Engineering Department of the Aristotle University of Thessaloniki, Greece. He is currently post-doctoral scholar at Institute of Chemical Engineering Sciences, Patras, Greece. He works in the eld of Continuum Mechanics/Applied Mathematics and focuses on thin lms and dislocations/plasticity problems.

References [1] D. Sfyris, G.I. Sfyris, C. Galiotis, "Curvature dependent surface energy for free standing monolayer graphene: some closed form solutions of the nonlinear theory". International Journal of Nonlinear Mechanics, 67, 186-197 (2014). [2] D. Sfyris, "Phonon, Cauchy-Born and homogenized stability criteria for a free-standing monolayer graphene at the continuum level". European Journal of Mechanics A/Solids, 55, 134-148 (2016) . [3] D. Sfyris, "Twinning mechanism and habit lines in monolayer-thick free-standing graphene: theoretical predictions". International Journal of Engineering Science, 113 (2017) 1-19.

RAM3 Workshop

Rome, 22-24 November 2017