Incorporation of the first gradient of strain, in addition to the strain itself, into the strain energy
density of an elastic solid leads to Mindlin's first strain gradient theory, which is useful for
examination of size effect as well as other mechanical phenomena at the nano-scale. For
isotropic elastic solids, the first strain gradient theory, in addition to the two independent
Lamé constants, gives rise to five new material constants which in turn reduce to two
material parameters, ℓ1 and ℓ2 with dimension of length. The evaluation of these …