Size-dependent effective properties of a heterogeneous material with interface energy effect: from finite deformation theory to infinitesimal strain analysis

In this paper, the change of the elastic fields induced by the interface energies and the interface stresses from the reference configuration to the current configuration is considered. It is emphasized that the governing equations taking into account the interface energy effect should be established within the framework of finite deformation in the first place, and then the approximations of governing equations for a finitely deformed multi-phase elastic medium by an infinitesimal strain analysis can be formulated. Hence it can be seen that the asymmetric interface stress has to be used in the Young-Laplace equation. According to the above mentioned formalism, analytical expressions of the size-dependent effective moduli of a particle-filled composite material with interface energy effect are derived. It is shown that, different from the results obtained by previous researchers, the liquid-like surface/interface tension, as a residual stress-type term, also influences the effective property of the composite.