**Quasi-analytical solution for the stable system of the multi-layer
folded graphene wrinkles**

YC Zhang and N Wei and JH Zhao and YD Gong and T Rabczuk, JOURNAL OF APPLIED PHYSICS, 114, 063511 (2013).

DOI: 10.1063/1.4817768

A quasi-analytical solution on the minimum length and its corresponding system energy is proposed for the stable multi-layer folded graphene wrinkles (FGWs). The quasi-analytical solution shows that: (1) at a certain threshold height, a single-layer FGW becomes energetically favorable compared to a standing graphene wrinkle. (2) All the geometrical properties of single-layer FGW reproduce in the double-layer FGWs, which is considered as the typical configuration for predicting the multi-layer folded FGWs. (3) Parametric studies show that the increased bending stiffness per length promotes the minimum graphene length while the case is reversed for the increased adhesion energy density. Both of the increased bending stiffness per length and adhesion energy density lead to the decreased system energy for the stable folded structure, while the system energy is less sensitive to the variation of adhesion energy density compared to that of the bending stiffness per length. Besides, molecular mechanics simulation shows that the present model has high accuracy on evaluating the system energy and the configuration for multi-layer FGWs. (C) 2013 AIP Publishing LLC.

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