Invariant-based visco-hyperelasticity of isotropic materials

In this study the invariant-based formulation of visco-hyperelasticity is analyzed in terms of its ability to capture the mechanical response of polymeric materials. The finite element implementation of the considered constitutive relationships is discussed in detail as well. The derived equations of the uniaxial tension (UT) and the equibiaxial tension (EBT) processes have been utilized to determine the material parameters for polyethylene terephthalate (PET) by using a leasts quares optimization procedure which incorporates simultaneously both UT and EBT data measured for various strain rates. It is demonstrated that a satisfactory curve-fitting result has been achieved with a relatively simple model utilizing the stored-energy function as proposed by Biderman. Moreover, a new simplified form of the fourth-order elasticity tensor for the invariant-based slightly compressible hyperelastic materials has been derived and subsequently used for the finite element (FE) implementation of the considered class of visco-hyperelastic (VE) constitutive equations. A general purpose user subroutine UMAT (UserMATerial) has been developed for the non-commercial FE program CalculiX.This subroutine allows one to implement into CalculiX any VE constitutive model utilizing user-specified volumetric and isochoric invariant-based stored-energy functions. The number of Maxwell elements responsible for the viscous behavior can be easily modified as well. Numerous validation tests have been conducted in order to check the performance of the developed UMAT code. Selected simulation results are presented in this work. The UMAT subroutine is attached as a supplementary material.