Curvature-dependent interfacial energy and its effects on the elastic properties of nanomaterials

Material interfaces can be regarded as two dimensional curved surfaces since their thickness is negligibly small in comparison with their planar dimensions. Experiments and materials simulation have demonstrated that the elastic energy of interface depends not only on its strain but also on its curvature. In this paper, first, the curvature-dependence of interfacial energy is studied and an interfacial energy formula is formulated, which has simple form and clear physical meanings. Next, a linear small deformation interface stress model is developed. It considers the curvature effect on interfacial energy and suggests that it would be convenient and advantageous to employ the Lagrangian description-based fundamental equations of the interface to study interface problems, especially the effect of residual interface stress. Then, a micromechanics framework considering both the interface effect and particle size distribution is proposed to predict the overall elastic properties of nanocomposites. Finally, the developed interface model and micromechanics approach are applied to study the effective modulus of nanoparticle reinforced composites. The results show that the curvature effect causes a much stronger size dependence of the effective modulus and the influence of particle size distribution becomes obvious when the dispersion of the particle radius is large.