Surface and size effects on the mechanical response of plates with a view to porous materials

Abstract

We investigate the effect of the thickness of plates made of a Lennard Jones FCC crystal subjected to tension with molecular simulations. The global elastic response of the plate depends on its thickness. The Young's modulus and Poisson's ratio are increasing with the thickness of the plate. Stress distributions across the thickness of the plate are calculated with a local version of the method of planes. The stress distributions for unloaded plates exhibit in-plane tensile stresses nearby the free surfaces, referred to as the interface stress, in the first layers of atoms. Upon mechanical loading, the elastic response of the plate is shown approximatively the superposition of standard linear elasticity to an initial state of stress that account for the surface effect. A slight decrease of stress is observed near the free surface. An interface stress that is independent of the thickness of the plate cannot be obtained unless the thickness of the plate is large enough. In a similar way, the cleavage energy required to break the plate into strips is not independent from the thickness of the plate. It decreases with decreasing thickness. Finally, the cleavage energy of a porous material made of hexagonal cells containing voids is obtained qualitatively. It depends on the void ratio, but also on the void size. The methodology and results discussed in this paper may enlighten future extended continuum theories.