Equivalent modulus of nanoporous materials based on Steigman-Ogden surface model

Abstract

The work of this paper mainly includes two parts. The first part is to simplify the stress boundary equation of the complex Steigmann-Ogden surface model expressed by the surface gradient operator in spherical coordinates to the stress boundary equation expressed by the spatial gradient operator according to the surface projection tensor. This simplification can directly substitute the complex formula into the fingermark method and directly calculate it into the sizeable mathematical calculation software. In the second part, based on the Mori-Tanaka hole model, the displacement field is decoupled into a hydrostatic and partial displacement field. Based on the homogenization approach, the equivalent elastic modulus of nanoporous materials is solved by satisfying the displacement boundary equation on the boundary of the representative volume element (RVE). The hydrostatic displacement field corresponds to the macroscopic equivalent bulk modulus, while the offset displacement field corresponds to the macroscopic equivalent shear modulus. Finally, this paper conducted auspicious numerical experiments on various surface elastic parameters and explored their control mechanisms. The research in this paper can provide a theoretical basis for designing and manufacturing nanoporous materials.