Application of a Gradient Elasticity Model to Interpret Size Effects in Uniaxial Loading

A special model of gradient elasticity theory is used to interpret the size effect, i.e. the dependence of material behavior on the specimen's dimensions, observed in perforated specimens under uniaxial loading. The specimens are assumed to be thin plates of infinite extent containing central circular holes of varying diameter. Equilibrium and compatibility equations along with appropriate boundary conditions are employed within a higher-order elasticity framework to obtain analytical solutions which, in the sequel, are used to derive explicit expressions for the stress concentration factor and compare these results with corresponding expressions derived in the literature for other types of generalized elasticity models including couple stress and micropolar theories. Finally, a comparison between the predictions of the present theory and recent experimental results for the strength of a perforated polycrystalline silicon MEMS specimen, is established in support of the simplified gradient model proposed.