Far-field analytical solution of composite materials considering steigmann-ogden surface

This paper presents an analytical solution for two-dimensional heterogeneous materials containing nano-fibers or pores, taking into account the Steigmann-Ogden elastic surface under far-field loading. The solution is validated against numerical results from the complex function method in recent literature, and the closed-form expressions for specific displacement and stress fields are provided. The effects of surface elasticity parameters, surface residual stress, fiber/pore size, and far-field load on local stress distribution are numerically investigated. Results show that surface elasticity parameters can disturb internal stresses within the fiber domain, while surface bending stiffness parameters significantly impact stress concentrations, which is different from the uniform stress distribution in the classical Eshelby problem. The analytical expressions reveal interesting phenomena, e.g., the stress/displacement fields of fiber composites under hydrostatic load are only related to the surface Lamé parameters, and the non-constant coefficient in the analytical expression under shear load is kept twice of that under uniaxial tensile load, which are first reported in this paper. The developed solution is crucial for accurately capturing the mechanical responses of nanocomposites with significant surface effects.