Paul Miles

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.

Uncertainty Analysis of a Finite Deformation Viscoelastic Model

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.Copyright

Uncertainty analysis of continuum scale ferroelectric energy landscapes using density functional theory

Density functional theory (DFT) provides exceptional predictions of material properties of ideal crystal structures such as elastic modulus and dielectric constants. This includes ferroelectric crystals where excellent predictions of spontaneous polarization, lattice strain, and elastic moduli have been predicted using DFT. Less analysis has focused on quantifying uncertainty of the energy landscape over a broad range of polarization states in ferroelectric materials. This is non-trivial because the degrees of freedom contained within a unit cell are reduced to a single vector order parameter which is normally polarization. For example, lead titanate contains five atoms and 15 degrees of freedom of atomic nuclei motion which contribute to the overall unit cell polarization. Bayesian statistics is used to identify the uncertainty and propagation of error of a continuum scale, Landau energy function for lead titanate. Uncertainty in different parameters is quantified and this uncertainty is propagated through the model to illustrate error propagation over the energy surface. Such results are shown to have an impact in integration of quantum simulations within a ferroelectric phase field continuum modeling framework.

Uncertainty Analysis of Dielectric Elastomer Membranes Under Multi-Axial Loading

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.Copyright

Experimental Investigation of Bicycle Frame FEA 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.Copyright