Static Mechanical Analysis of Nanobeams Reinforced with Graphene Nanoplatelets Using Modified Couple Stress Theory

Resumo

Composite materials are fundamental in contemporary engineering, standing out for their ability to combine different raw materials to create new materials with superior properties. Graphene, characterized by its flat two-dimensional (2D) carbon monolayer structure with a thickness of 0.34 nm, has aroused considerable interest due to its remarkable mechanical, thermal, and electrical properties. In particular, graphene derivatives, such as graphene nanoplatelets (GNP) and carbon nanotubes (CNT), have been widely explored as reinforcements in composites. Compared to CNT, GNP offers a more economical alternative and a greater surface area, available in various sizes, from nanometers to micrometers. Micro- and nanoscale composites serve as models for assessing material performance in multiple industries, such as automobiles, aviation, medicine, and construction, especially in cases where experimental methods are costly. Modeling and simulation techniques are employed to mitigate the costs associated with experimentation, from quantum mechanics to continuum mechanics. This work proposes a variational formulation to model the static mechanical behavior of nanobeams reinforced with graphene nanoplatelets. The micromechanical constitutive model modified Couple Stress, coupled with high-order beam kinematics, is developed to obtain the governing equations and their boundary conditions. The Navier procedure is utilized to develop an analytical solution to the problem. The results are compared with the literature, and the proposed model is proven accurate.