An analytical model for predicting equivalent elastic moduli of micro/nano-honeycombs with nonlocal effects

Abstract

When the structural size of honeycomb enters micro/nano scale, the influence of nonlocal effects on the mechanical responses becomes non-negligible, which should be taken into account when evaluate the mechanical properties of micro/nano-honeycombs. To this end, a novel method for predicting the equivalent elastic moduli of micro/nano-honeycombs is proposed. In this method, the two-phase local/nonlocal model is introduced into the constitutive equations and the analytical solution of the equivalent moduli is derived according to the energy equivalent principle. It is illustrated by the numerical examples that the results of the present method are lower than those of the classical elasticity theory, which is consistent with the phenomena observed in the experiment, effectively showing the nonlocal effects. The magnitude of nonlocal effects can be influenced by the geometrical size of the honeycomb. The smaller the geometric size of the honeycomb is, the more significant the nonlocal effects are. With the increase of the geometrical size of honeycomb, the nonlocal effects gradually weaken, and the numerical values predicted by the present method gradually approach the equivalent moduli values of the macro-scale honeycombs. Hence the present method has a good universality that can be used in both macro and micro/nano scale honeycombs.