On the yield criterion of porous materials by the homogenization approach and Steigmann--Ogden surface model

Abstract

In this work, we investigate the yield criterion of nanoporous materials by using homogenization approach and Steigmann--Ogden surface model. The representative volume element (RVE) is proposed as an infinite matrix containing a tiny nanovoid. The matrix is incompressible, rigid-perfectly plastic, von Mises materials and nanovoids are dilute and equal in size. First, the constitutive of microscopic stress and microscopic strain rate is established based on the flow criterion. Secondly, according to the Hill's lemma, the relationship between the macroscopic equivalent modulus and the microscopic equivalent modulus is established by homogenization approach. Thirdly, the macroscopic equivalent modulus containing the Steigmann--Ogden surface model including surface parameters, porosity and nanovoid radius is derived from the trial microscopic velocity field. Finally, an implicit macroscopic strength criterion for nanoporous materials is developed. For surface modulus, nanovoids radius and porosity studies are developed through extensive numerical experiments. The research results in this paper have reference significance for the design and manufacture of nanoporous materials.