Bayesian uncertainty analysis of finite deformation viscoelasticity. (December 2015) - Miles, Paul; Hays, Michael; Smith, Ralph; Oates, William
Highlights: Experimentally characterize viscoelasticity of the dielectric elastomer, VHB 4910. Apply Bayesian techniques to analyze and quantify model uncertainty. Nonlinear viscoelasticity more accurately predicted elastomer behavior. Viscoelastic time constant varied with the deformation rate following a power law. Abstract: The viscoelasticity of the dielectric elastomer, VHB 4910, is experimentally characterized, modeled, and analyzed using Bayesian uncertainty analysis. Whereas these materials are known for their large-field induced deformation and broad applications in smart structures, the rate-dependent viscoelastic effects are not well understood. To address this issue, we quantify both the hyperelastic and viscoelastic constitutive behavior and use Bayesian uncertainty analysis to assess several key modeling attributes. Specifically, we compare an Ogden-based phenomenological model to a nonaffine hyperelastic model and couple hyperelasticity to both linear and nonlinear viscoelasticity. The utilization of Bayesian statistics is shown to provide insight into quantifying nonlinear viscoelasticity behavior as a function of internal state variables. The results are validated experimentally in the finite deformation regime over a range of stretch rates spanning four orders of magnitude ( 6.7 × 10 - 5 –0.67 Hz). A unique set of hyperelastic parameters are identified, independent of the stretch rate. In addition, comparisons of the linear and nonlinear viscoelastic models demonstrate a reduction in modeling error by approximately a factor of three. Finally, the viscoelastic time constant is shown to produce an inverse stretch rate power law dependence regardless of which hyperelastic model is used.