On the development of compressible pseudo-strain energy density for elastomers: Part 2 application to finite element

Abstract

This paper presents the results of a finite element procedure and analysis for pure gum rubber, based on a compressible strain energy function proposed by the authors. The development of the proposed separable, one-term compressible constitutive equations is explained. An explanation of the isochoric part of the strain energy function based on constitutive relation proposed by the authors is also discussed. A brief review of material properties and the basic equations of the finite element procedure are given. Fortran 77 was used to code the user-subroutine that calculates the element's isochoric tangent stiffness and isochoric first Piola-Kirchhoff stress from the proposed one-term strain energy density function. The subroutine was then implemented into a commercial finite element package. The Updated Lagrangian (UL) procedure was used, based on the principal stretch ratios in which the material moduli are initially determined in the principal direction and then transformed to the local coordinate. The results of the finite element analysis based on the Ogden and the proposed models were compared against the experimental data. It is shown that although the Ogden model produced an accurate result, the proposed model improves the results on two fronts. Firstly, the accuracy of the results is slightly increased in the uniaxial case and more noticeably so in the equibiaxial analysis. Secondly, the proposed model improved the analysis run-time by approximately 50%. In short, it was shown that the proposed one-term model exhibited a better representation of the material behavior.