Modelling porous structures by penalty approach in the extended finite element method

Abstract

In this study, a methodology for studying porous structures was proposed. The extended finite element method (XFEM) in conjunction with a penalty approach was used to model the porous structures. The holes were considered to have very small Young's modulus, thus they could be treated as inclusions in a matrix. The level set method was applied to describe the internal boundaries of the holes. Various porous structures were investigated. A practical example of the porous structures, which was the microstructure of a trabecular bone, was examined to show the capability of the proposed methodology. The aim of the study was to demonstrate that various complicated porous structures can be modelled efficiently by the XFEM without any major modification to the existing formula.

Keywords:

• extended finite element method
• porous
• bone
• penalty
• level set