A formulation for the characteristic lengths of fcc materials in first strain gradient elasticity via the Sutton–Chen potential

Abstract

The usual continuum theories are inadequate in predicting the mechanical behavior of solids in the presence of small defects and stress concentrators; it is well known that such continuum methods are unable to detect the change of the size of the inhomogeneities and defects. For these reasons various augmented continuum theories and strain gradient theories have been proposed in the literature. The major difficulty in implication of these theories lies in the lack of information about the additional material constants which appear in such theories. For fcc metals, for the calculation of the associated characteristic lengths which arise in first strain gradient theory, an atomistic approach based on the Sutton–Chen interatomic potential function is proposed. For the validity of the computed characteristic lengths, the phenomenon of the size effect pertinent to a nano-sized circular void within an fcc (111) plane is examined via both first strain gradient theory and lattice statics. Comparison of the results explains the physical ramifications of the characteristic lengths in improving the usual continuum results. Moreover, by reconsideration of the Kelvin problem it is shown that a commonly employed variant of the first strain gradient theory is only valid for a few fcc metals.