Study on Compressibility Control of Hyperelastic Material in Homogenization Method Using Mixed Finite Element Analysis

Abstract

It is well known that the compressibility or incompressibility of biological tissue stems from its microscopic structure, which is in general composed of varied material compressibility including incompressibility. This paper proposes a framework of homogenization method in which compressibility/incompressibility of the macrostructure properly reflects those of the microstructure. The formulation is based on the mixed variational principle with perturbed Lagrange-multiplier. It is shown that the rate of volumetric change of the macrostructure can be controlled through the homogenization procedure by introducing the constraint only for the microstructure. A couple of numerical examples is given so as to demonstrate the validity of the proposed method. By comparing the numerical results with theoretical solutions, the method is also confirmed to be free from locking.