The implementation for large strain viscoelasticity follows the derivation by Holzapfel (Ref. 1).

The strain energy in the main hyperelastic branch is normally denoted with the superscript ∞ to denote the long-term equilibrium (as ).

where the auxiliary second Piola-Kirchhoff stress tensors Qm are defined as

The time evolution of the auxiliary stress tensor Qm in each viscoelastic branch is given by the rate

here, Siso,m is the isochoric second Piola-Kirchhoff stress tensor in the branch m. These tensors are derived from the strain energy density in the main hyperelastic branch and the energy factors βm as

so the time evolution of the auxiliary stress tensor Qm is given by

the time evolution of the auxiliary stress tensor qm reads

The same options for defining Temperature Effects as described for Linear Viscoelastic Materials are available for large strain viscoelasticity.