Finite element implementation including sensitivity analysis of a simple finite strain viscoelastic constitutive law

This article describes the implementation of a finite strain viscous hyper-elastic material law into a finite element code. The material model is made up of a Maxwell element in parallel with a spring. Both springs represent hyper-elastic material behaviour, and compressibility is taken into account. In addition to that, the sensitivity analysis using direct differentiation is described extensively. The implementation is verified by three test cases, uniaxial tension, pure shear and indentation testing. The sensitivity analysis by direct differentiation is validated by comparison against results obtained by a finite difference scheme.