Uncertainty quantification and stochastic-based viscoelastic modeling of finite deformation elastomers

Material parameter uncertainty is a key aspect of model development. Here we quantify parameter uncertainty of a viscoelastic model through validation on rate dependent deformation of a dielectric elastomer that undergoes finite deformation. These materials are known for there large field induced deformation and applications in smart structures, although the rate dependent viscoelastic effects are not well understood. To address this issue, we first quantify hyperelastic and viscoelastic model uncertainty using Bayesian statistics by comparing a linear viscoelastic model to uniaxial rate dependent experiments. The probability densities, obtained from the Bayesian statistics, are then used to formulate a refined model that incorporates the probability densities directly within the model using homogenization methods. We focus on the uncertainty of the viscoelastic aspect of the model to show under what regimes does the stochastic homogenization framework provides improvements in predicting viscoelastic constitutive behavior. It is show that VHB has a relatively narrow probability distribution on the viscoelastic time constants. This supports use of a discrete viscoelastic model over the homogenized model.

[1]  Ralph C. Smith,et al.  Experimental Implementation of a Hybrid Nonlinear Control Design for Magnetostrictive Actuators , 2009 .

[2]  Kurt Kremer,et al.  Dynamics of entangled flexible polymers. Monte Carlo simulations and their interpretation , 1983 .

[3]  T. Trucano,et al.  Verification, Validation, and Predictive Capability in Computational Engineering and Physics , 2004 .

[4]  K. Tanie,et al.  Biomimetic soft actuator: design, modeling, control, and applications , 2005, IEEE/ASME Transactions on Mechatronics.

[5]  Gerhard A. Holzapfel,et al.  Nonlinear Solid Mechanics: A Continuum Approach for Engineering Science , 2000 .

[6]  Heikki Haario,et al.  DRAM: Efficient adaptive MCMC , 2006, Stat. Comput..

[7]  R. Christensen A Nonlinear Theory of Viscoelasticity for Application to Elastomers , 1980 .

[8]  H. Haario,et al.  An adaptive Metropolis algorithm , 2001 .

[9]  Duncan W. Haldane,et al.  Field Driven Stiffness Control of Legged Robotic Structures Using Dielectric Elastomers , 2011 .

[10]  Ralph C. Smith,et al.  Optimal Tracking Using Magnetostrictive Actuators Operating in Nonlinear and Hysteretic Regimes , 2005 .

[11]  Y. Bar-Cohen,et al.  Electroactive Polymer Actuators and Sensors , 2008 .

[12]  Ralph C. Smith,et al.  Smart material systems - model development , 2005, Frontiers in applied mathematics.

[13]  Gerhard A. Holzapfel,et al.  ON LARGE STRAIN VISCOELASTICITY: CONTINUUM FORMULATION AND FINITE ELEMENT APPLICATIONS TO ELASTOMERIC STRUCTURES , 1996 .

[14]  T. C. B. McLeish,et al.  Polymer Physics , 2009, Encyclopedia of Complexity and Systems Science.

[15]  Todd A. Gisby,et al.  Multi-functional dielectric elastomer artificial muscles for soft and smart machines , 2012 .

[16]  Mary C. Boyce,et al.  Constitutive modeling of the large strain time-dependent behavior of elastomers , 1998 .

[17]  J. H. Weiner,et al.  Statistical Mechanics of Elasticity , 1983 .