IJE TRANSACTIONS C: Aspects Vol. 31, No. 3 (March 2018) 456-463    Article in Press

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S. Safarian and M. Tahani
( Received: August 13, 2017 – Accepted in Revised Form: October 12, 2017 )

Abstract    In this paper, an atomistic based finite element model is developed to investigate the influence of topological defects on mechanical properties of graphene. The general in-plane stiffness matrix of the hexagonal network structure of graphene is found. Effective elastic modulus of a carbon ring is determined from the equivalence of molecular potential energy related to stretch and angular deformation. A hexagonal carbon ring as a unit cell of graphene sheets is modeled by four-node elements and by applying three-node triangular elements, Stone-Wales (SW) defect as an important topological defect which leads to the formation of two heptagons and pentagons is modeled. In this method, both pristine structure of graphene and graphene with SW defect are considered and to get more real structure, an atomistic model of a small part of graphite sheet around the defect site, is modeled in Gaussian software and new arrangement around SW defect are obtained by minimizing its energy. Young’s modulus, shear modulus and Poisson’s ratio of the pristine single-layered graphene sheet (SLGS) and the effect of topological defects on the elastic properties of SLGS is examined. The numerical results from this new model show good agreement with data available in the literature.


Keywords    Graphene sheet, Defects, Atomistic model, Finite element method, Elastic properties


چکیده    عیوب ساختاری که پیدایش آن ها در طی فرآیندهای سنتز و خالص­سازی اجتناب ناپذیر بوده، بر روی خواص گرافن تاثیر می گذارند. در این مقاله مدل جدید هیبریدی اتمی – پیوسته به منظور مطالعه اثرات عیوب ساختاری بر روی خواص مکانیکی گرافن معرفی شده است. طی یک تحلیل محیط پیوسته ماتریس سختی برای ساختار شبکه ای گرافن محاسبه شده است. از این رو حلقه شش گوشه­ای کربن به عنوان نماینده گرافن با یک مدل جدید شامل المان­های چهار نقطه­ای و در قسمت عیب با المان­های مثلثی مدل شده است. این ترکیب کمک می­کند که بتوان هر ساختاری شامل المان­های شش گوشه­ای کربن را شبیه سازی کرد. با وجود در نظر گرفتن تمامی اندرکنش­های پیوندی و غیرپیوندی حجم محاسبات و تعداد المان­ها کم شده است. در تحقیقات گذشته تغییر شکل­های موضعی اتمی در اطراف محل عیب در نظر گرفته نشده که این در واقع نمی­تواند درست باشد چراکه آرایش اتمی در اطراف عیب بهم می­ریزد. برای این منظور از نرم افزار Gaussian برای پیدا کردن موقعیت دقیق اتم­های اطراف عیب استفاده شده است. در نهایت مدول الاستیسته، مدول برشی و نسبت پواسون برای ساختارگرافن کامل و معیوب محاسبه شده است.

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