Investigation of the nonlinear hyper-viscoelastic behavior of elastomers at finite strain: implementation and numerical validation

Rubber-like materials are known for their time-dependent behavior. The ability to model the hyperviscoelastic behavior of a diverse range of these materials including polymers, elastomers and rubbers is of increasing importance especially in the context of soft tissue mechanics. In this paper, a viscohyperelastic model, recently published, is recalled. The implementation of this hyperviscoelastic model at finite strain into the finite element software Abaqus via a umat subroutine is presented. To this end, the discrete form of the constitutive equations of the stress and the tangent modulus following the Jaumann derivative were determined. Then, the implementation was validated using homogeneous tests of simple extension and simple shear for several history of strain and non-homogeneous test of pure torsion of a hollow cylinder. The semi-analytic resolution of the boundary value problems of each test compared to the results of simulation of the implemented model shows a total validation of the implementation algorithm. The implemented model can, therefore, be used in real engineering and biomechanical applications dealing with hyperviscoelastic models.

Automated summary

This paper presents an implementation method for a viscohyperelastic model and validates its accuracy through various tests. The implemented model can be applied to engineering and biomechanical applications dealing with hyperviscoelastic models.