Numerical homogenization for incompressible materials using selective smoothed finite element method

Composite materials with periodic microstructures are commonly used in engineering. Numerical homogenization with finite element method (FEM) has proven fairly effective to determine the mechanical properties of a range of composite materials. However, traditional FEM fails to evaluate the effective mechanical properties for incompressible constituents due to volumetric locking problem in numerical analysis. In this paper, a novel selective smoothed finite element method (S-FEM) in multi-material domain using triangular and tetrahedral elements is proposed to overcome the locking problem in the numerical homogenization of incompressible materials. The implementation of S-FEM is easy without additional parameters. A number of characterization examples for porous, multiphase, tissue scaffold composites are presented to demonstrate the effectiveness of the proposed SFEM homogenization in handling incompressible base materials.