Dielectric elastomers are employed on a wide variety of adaptive structures. Many of these soft elastomers exhibit significant rate-dependencies in their response. Accurately quantifying this viscoelastic behavior is non-trivial and in many instances a nonlinear modeling framework is required. Fractional-order operators have been applied to modeling viscoelastic behavior for many years, and recent research has shown fractional-order methods to be effective for nonlinear frameworks. This implementation can become computationally expensive to achieve an accurate approximation of the fractional-order derivative. In this paper, we demonstrate the effectiveness of using quadrature techniques in approximating the Riemann-Liouville definition for fractional derivatives in the context of developing a nonlinear viscoelastic model.

Ferroelectric materials exhibit strong electromechanical behavior which has led to the production of a wide variety of adaptive structures and intelligent systems, ranging from structural health monitoring sensors, energy harvesting circuits, and flow control actuators. Given the large number of applications, accurate prediction of ferroelectric materials constitutive behavior is critical. This presents many challenges, including the need to predict behavior from electronic structures up to macroscropic continuum. Many of the structure-property relations in these materials can be accurately calculated using density functional theory (DFT). However, DFT is not necessarily conducive to the large scale computations required to solve these problems on a continuum scale. Introducing a phase field polarization order parameter is an alternative approach, which provides a means to simulate the length scale gap between nano- and microscale domain structure evolution. The introduction of the phase field approximation results in uncertainty. Bayesian statistical analysis is an ideal tool for quantifying the uncertainty associated with the continuum phase field model parameters. Analyses of monodomain structures allows for identification of Landau energy and electrostrictive stress parameters. Identifying the exchange parameters, which are proportional to the polarization gradients, requires consideration of polydomain structures. This is a nontrivial problem as domain wall structures are fully coupled between the Landau energy, electrostrictive, and exchange parameters. Accurately quantifying the uncertainty in the phase field parameters will provide insight into the nonlinear constitutive behavior.

We consider subset selection and active subspace techniques for parameters in a continuum phase-field polydomain model for ferroelectric materials. This analysis is necessary to mathematically determine the parameter subset or subspace critically affecting the response, prior to model calibration using either experimental or synthetic data constructed using density functional theory (DFT) simulations. For the 180° domain wall model, we employ identifiability analysis using a Fisher information matrix methodology, and subspace selection to determine the active subspace. We demonstrate the implementation and interpretation of techniques that accommodate the model structure and discuss results in the context of identifiable parameter subsets and active subspaces quantifying the strongest influence on the model output. Our results indicate that the governing domain wall gradient energy exchange parameter is most identifiable.

We perform global sensitivity analysis for parameters in a continuum energy model for ferroelectric materials, which is informed by density functional theory (DFT). Specifically, we use global sensitivity analysis to rank the sensitivity of phenomeno-logical parameters governing the Landau and electrostriction energy for single-domain ferroelectric lead titanate. These techniques include Pearson correlations constructed directly from input and output relations, Sobol sensitivity indices, and Morris indices.

A variety of models have been developed to simulate the behavior of electroactive elastomers. As with all modeling applications, there are varying levels of uncertainty associated with measurement limitations and lack of knowledge of the constitutive behavior. Methods of quantifying this uncertainty have been explored previously using Bayesian statistics under uniaxial mechanical loading. The research presented here expands prior developments to quantify constitutive model uncertainty under multi-axial mechanical loading at different electrostatic fields. Specifically, we experimentally characterize and simulate transverse loading of a pre-stretched membrane under different electrostatic fields. We also quantify the dielectric response from electric displacement versus electric field loops. Bayesian statistical methods are employed to quantify modeling uncertainties in light of the data conducted on the 3M elastomer, VHB 4910.

The viscoelasticity of the dielectric elastomer, VHB 4910, is experimentally characterized, modeled, and analyzed using uncertainty quantification. These materials are known for their 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 by comparing a finite deformation viscoelastic model to uni-axial rate dependent experiments. The utilization of Bayesian statistics is shown to provide additional insight into different viscoelastic processes within elastomers. This is demonstrated by coupling two hyperelastic models, an Ogden model and a nonaffine model, to different types of viscoelastic models.

This study experimentally investigated pedal cycle frame loads and verified analytical load cases applied to vehicle design. The experimental results were compared with a Finite Element Analysis (FEA) model. The weight of the rider on the seat, road induced loads and vibrations, and the force the rider exerts on the pedals affect the stress state of the frame. Strain gauges were applied to two different frame models. Four different locations were tested on a monotube long-wheel base (LWB) recumbent frame and six locations on a standard upright Schwinn. The stress state was calculated from the raw strain data. Depending on the gauge being used, the results either indicated the von Mises stress or simply the axial stress. The different loading conditions tested were as follows: static, steady pedaling on smooth, mid-grade, and rough pavement, and hard acceleration on level ground and uphill. The static and hard acceleration cases were directly compared to the FEA model. The experimental results were comparable to the FEA analysis. The complexity of the load case, coupled with unknown actual loads, explains the larger differences between FEA and experimental results. Based on experimental results, the FEA model was refined, improving the agreement between model and experiment. The stress states of a bicycle frame were successfully found experimentally, being confirmed by multiple runs under each loading condition. Based on the agreement between the two methods, the use of FEA load cases to predict stresses in pedal cycle frames was verified.