This paper presents an investigation on the out-of-plane behaviour of graphene when cyclically loaded in-plane. Using an atomistic finite element approach, previous developed and validated by the authors, the stress-strain behaviour of graphene is evaluated under different cyclic loading tests (uniaxial, biaxial, shear). To simulate the bonds between carbon-carbon (C–C) atoms, beam elements are used, with their stiffness being described by the Morse potential associated to an elastoplastic law. Monotonic and hysteretic tests are performed and a comparison with the in-plane behaviour results, recently obtained, is accomplished. The instabilities of graphene, that occur in compression, are discussed and the buckling stresses are compared with those calculated from simple analytical formulae. The graphene failure modes obtained are also analysed. Finally, some concluding remarks are drawn about the main differences between the monotonic and hysteretic behaviour, as well as the in-plane and out-of-plane ones.

本文对循环加载面内石墨烯的面外行为进行了研究。作者使用先前开发和验证的原子有限元方法，在不同的循环载荷试验（单轴，双轴，剪切）下评估了石墨烯的应力-应变行为。为了模拟碳-碳（CC）原子之间的键，使用了梁单元，其刚度由与弹塑性定律相关的莫尔斯电势描述。进行了单调和滞后测试，并与最近获得的平面内行为结果进行了比较。讨论了压缩中发生的石墨烯不稳定性，并将屈曲应力与根据简单分析公式计算出的屈曲应力进行了比较。还分析了获得的石墨烯破坏模式。