Fully anisotropic finite strain viscoelasticity based on a reverse multiplicative decomposition and logarithmic strains

• We present a novel formulation for fully anisotropic finite strain viscoelasticity.
• It is based on a reversed multiplicative decomposition respect to Sidoroff’s proposal.
• The stored energy includes anisotropic equilibrated and non-equilibrated addends.
• The viscosities employed in the formulation may also be anisotropic.
• Examples show applicability of the model to finite element simulations.

In this paper we present a novel formulation for phenomenological anisotropic finite visco-hyperelasticity. The formulation is based on a multiplicative decomposition of the equilibrated deformation gradient into nonequilibrated elastic and viscous contributions. The proposal in this paper is a decomposition reversed respect to that from Sidoroff allowing for anisotropic viscous contributions. Independent anisotropic stored energies are employed for equilibrated and non-equilibrated parts. The formulation uses logarithmic strain measures in order to be teamed with spline-based hyperelasticity. Some examples compare the results with formulations that use the Sidoroff decomposition and also show the enhanced capabilities of the present model.