A viscoelastic constitutive model for compressible polymers based on logarithmic strain and its finite element implementation

In this paper, employing the logarithmic (or Hencky) strain as a more physical measure of strain, the time-dependent response of compressible viscoelastic materials is investigated. In this regard, we present a phenomenological finite strain viscoelastic constitutive model, developed within the framework of irreversible thermodynamics with internal variables. The formulation is based on the multiplicative decomposition of the deformation gradient into elastic and viscoelastic parts, together with the use of the isotropic property of the Helmholtz strain energy function. Making use of a logarithmic mapping, we present an appropriate form of the proposed constitutive equations in the time-discrete frame. Numerical examples are presented to show features of the new proposed model. In these examples, behavior of a bushing system under radial, torsional and combined radial–torsional loadings is studied. A very good agreement is observed between the predicted results and experimental data reported in the literature.

► A 3D viscoelastic constitutive model for compressible polymers based on logarithmic strain is proposed.
► Finite element implementation of the model is presented in detail (in an implicit form).
► Making use of a logarithmic mapping, an appropriate form of the proposed constitutive equations in the time-discrete frame is presented.
► The model is thermodynamically consistent.
► Behavior of a 3D bushing system under radial, torsional and combined radial–torsional loadings is studied and the predicted results are compared with those of experimental data.