Postbuckling analysis of multi-layered graphene sheets under non-uniform biaxial compression

In this article, the nonlinear buckling characteristics of multi-layered graphene sheets are investigated. The graphene sheet is modeled as an orthotropic nanoplate with size-dependent material properties. The graphene film is subjected by non-uniformly distributed in-plane load through its thickness. To include the small scale and the geometrical nonlinearity effects, the governing differential equations are derived based on the nonlocal elasticity theory in conjunction with the von Karman geometrical model. Explicit expressions for the postbuckling loads of single- and double-layered graphene sheets with simply supported edges under biaxial compression are obtained. For numerical results, six types of armchair and zigzag graphene sheets with different aspect ratio are considered. The present formulation and method of solution are validated by comparing the results, in the limit cases, with those available in the open literature. Excellent agreement between the obtained and available results is observed. Finally, the effects of nonlocal parameter, buckling mode number, compression ratio and non-uniform parameter on the postbuckling behavior of multi-layered graphene sheets are studied.

► Nonlinear stability of multi-layered graphene sheets is studied.
► Graphene sheet is subjected to non-uniform in-plane loading through its thickness.
► Small scale and nonlinearity effects are taken into consideration.
► Six types of armchair and zigzag graphene sheets are investigated.
► Postbuckling loads are intensely sensitive to non-uniform and nonlocal parameters.