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.
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Petiteau, JC., Verron, E., Othman, R. et al. Large strain rate-dependent response of elastomers at different strain rates: convolution integral vs. internal variable formulations. Mech Time-Depend Mater 17, 349–367 (2013). https://doi.org/10.1007/s11043-012-9188-7
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DOI: https://doi.org/10.1007/s11043-012-9188-7