Gradient Nanomechanics: Applications to Deformation, Fracture, and Diffusion in Nanopolycrystals

Abstract

The term “gradient nanomechanics” is used here to designate a generalized continuum mechanics framework accounting for “bulk-surface” interactions in the form of extra gradient terms that enter in the balance laws or the evolution equations of the relevant constitutive variables that govern behavior at the nanoscale. In the case of nanopolycrystals, the grain boundaries may be viewed either as sources/sinks of “effective” mass and internal force or as a separate phase, interacting with the bulk phase that it surrounds, and supporting its own fields, balance laws, and constitutive equations reflecting this interaction. In either view, a further common assumption introduced is that the constitutive interaction between bulk and “interface” phases enters in the form of higher order gradient terms, independently of the details of the underlying physical mechanisms that bring these terms about. The effectiveness of the approach is shown by considering certain benchmark problems for nanoelasticity, nanoplasticity, and nanodiffusion for which standard continuum mechanics theory fails to model the observed behavior. Its implications to interpreting size-dependent stress-strain curves for nanopolycrystals with varying grain size are also discussed.