Relation between strength and local stresses in nanostructures as a function of their size and shape

L Pizzagalli and R Gatti and J Amodeo and J Godet and J Durinck and S Brochard, JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS, 205, 106306 (2025).

DOI: 10.1016/j.jmps.2025.106306

The aim of this work is to understand how and why the strength of nanostructures depends on their size and shape. We performed extensive molecular dynamics simulations of the uniaxial compression of 2D FCC models with various sizes and shapes. It is found that the strength varies as a power law with size, with an exponent critically depending on shape. Plastic deformation is triggered by a unique mechanism, which is the nucleation of Shockley dislocation at local stress gradients in the vicinity of contact corners. This allows to unravel the effect of size and shape by examining the relation between local stresses and applied stress. Our analyses reveal that spatial variations of local stresses as a function of size and shape are complex and not simply related to the stress concentration as predicted by the elasticity theory. However, it is found that these local stresses linearly depend on the applied stress. Finally, we propose that the observed size effect on strength is caused by a screening interaction between the stress gradients occurring at all contact corners.

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