Abstract
Two different viscoelastic frameworks adapted to large strain rate-dependent response of elastomers are compared; for each approach, a simple model is derived. Within the Finite Linear Viscoelasticity theory, a time convolution integral model based on an extension to solid of the K-BKZ model is proposed. Considering the multiplicative split of the deformation gradient into elastic and inelastic parts, an internal variable model based on a large strain version of the Standard Linear Solid model is considered. In both cases, the strain energy functions involved are chosen neo-Hookean, and then each model possesses three material parameters: two stiffnesses and a viscosity parameter. These parameters are set to ensure the equivalence of the model responses for uniaxial large strain quasi-static and infinitely fast loading conditions, and for uniaxial rate-dependent small strain loading conditions. Considering their responses for different Eulerian strain rates, their differences are investigated with respect to the strain rate; more specifically, both stiffness and dissipative properties are studied. The comparison reveals that these two models differ significantly for intermediate strain rates, and a closing discussion highlights some issues about their foundations and numerical considerations.
Highlights
Elastomers are often used for damping parts in industrial applications because of their remarkable dissipative properties
We focus on the viscoelastic nature of its mechanical response and we consider two simple models: the former based on the convolution integral approach, and the latter based on internal variables theory
By examining the two models and their response at low and high strain rates, it appears that the parameters g0 in the Convolution Integral Model (CIM) and C1 in the Internal Variable Model (IVM) represent the stiffness for quasi-static loading conditions, and that the parameters g1 in the CIM and C2 in the IVM represent the additional stiffness reached at high strain rates
Summary
Elastomers are often used for damping parts in industrial applications because of their remarkable dissipative properties. The rate-dependent small strain response of elastomers is usually predicted in the general framework of linear viscoelasticity In this case, integral models issued from the Boltzmann superposition principle and the rheological Maxwell, Kelvin, Zener, Poynting–Thomson models are equivalent (Ferry 1980; Christensen 1982; Tschoegl 1989; Wineman and Rajagopal 2000). In this way, we derive two simple models for large strain viscoelasticity: the first one referred to as a Convolution Integral Model (CIM) is a solid extension of the K-BKZ model, and the second one, referred to as an Internal Variable Model (IVM), is the large strain counterpart of the Zener model as proposed by Huber and Tsakmakis (2000). For equivalent sets of material parameters, their uniaxial responses, i.e. their stiffness and associated dissipation, are compared and discussed with respect to the strain rate
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