Transformation of Test Data for the Specification of a Viscoelastic Marlow Model

Abstract

The combination of hyperelastic material models with viscoelasticity allows researchers to model the strain-rate-dependent large-strain response of elastomers. Model parameters can be identified using a uniaxial tensile test at a single strain rate and a relaxation test. They enable the prediction of the stress–strain behavior at different strain rates and other loadings like compression or shear. The Marlow model differs from most hyperelastic models by the concept not to use a small number of model parameters but a scalar function to define the mechanical properties. It can be defined conveniently by providing the stress–strain curve of a tensile test without need for parameter optimization. The uniaxial response of the model reproduces this curve exactly. The coupling of the Marlow model and viscoelasticity is an approach to create a strain-rate-dependent hyperelastic model which has good accuracy and is convenient to use. Unfortunately, in this combination, the Marlow model requires to specify the stress–strain curve for the instantaneous material response, while experimental data can be obtained only at finite strain rates. In this paper, a transformation of the finite strain rate data to the instantaneous material response is derived and numerically verified. Its implementation enables us to specify hyperelastic materials considering strain-rate dependence easily.

Nonlinear static analysis of truss core sandwich beams in three-point bending test

“…3 ) and can be decomposed into a deviatoric 𝑊 dev and a volumetric 𝑊 vol part (required for a compressible case only) as [21,39]:…”

“…In the hyperelastic theory the stress-strain relationship is derived from the strain energy potentials. In most cases, but not limited to, the energy potentials is described using the strain energy functions as Neo-Hookean [17], Mooney-Rivlin [18], Polynomial Form [19], Ogden [20], Marlow [21], Yeoh [22]. For a material under a combined load case the set of three static tests is required to correctly describe the hyperelastic material model.…”