@article{leon_miles_smith_oates_2019, title={Active subspace analysis and uncertainty quantification for a polydomain ferroelectric phase-field model}, volume={30}, ISSN={["1530-8138"]}, DOI={10.1177/1045389X19853636}, abstractNote={We perform parameter subset selection and uncertainty analysis for phase-field models that are applied to the ferroelectric material lead titanate. A motivating objective is to determine which parameters are influential in the sense that their uncertainties directly affect the uncertainty in the model response, and fix noninfluential parameters at nominal values for subsequent uncertainty propagation. We employ Bayesian inference to quantify the uncertainties of gradient exchange parameters governing 180° and 90° tetragonal phase domain wall energies. The uncertainties of influential parameters determined by parameter subset selection are then propagated through the models to obtain credible intervals when estimating energy densities quantifying polarization and strain across domain walls. The results illustrate various properties of Landau and electromechanical coupling parameters and their influence on domain wall interactions. We employ energy statistics, which quantify distances between statistical observations, to compare credible intervals constructed using a complete set of parameters against an influential subset of parameters. These intervals are obtained from the uncertainty propagation of the model input parameters on the domain wall energy densities. The investigation provides critical insight into the development of parameter subset selection, uncertainty quantification, and propagation methodologies for material modeling domain wall structure evolution, informed by density functional theory simulations.}, number={14}, journal={JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES}, author={Leon, Lider S. and Miles, Paul R. and Smith, Ralph C. and Oates, William S.}, year={2019}, month={Aug}, pages={2027–2051} }
 @article{miles_pash_smith_oates_2019, title={Global Sensitivity Analysis of Fractional-Order Viscoelasticity Models}, volume={10968}, ISSN={["1996-756X"]}, DOI={10.1117/12.2514160}, abstractNote={In this paper, we investigate hyperelastic and viscoelastic model parameters using Global Sensitivity Analysis (GSA). These models are used to characterize the physical response of many soft-elastomers, which are used in a wide variety of smart material applications. Recent research has shown the effectiveness of using fractionalorder calculus operators in modeling the viscoelastic response. The GSA is performed using parameter subset selection (PSS), which quantifies the relative parameter contributions to the linear and nonlinear, fractionalorder viscoelastic models. Calibration has been performed to quantify the model parameter uncertainty; however, this analysis has led to questions regarding parameter sensitivity and whether or not the parameters can be uniquely identified given the available data. By performing GSA we can determine which parameters are most influential in the model, and fix non-influential parameters at a nominal value. The model calibration can then be performed to quantify the uncertainty of the influential parameters.}, journal={BEHAVIOR AND MECHANICS OF MULTIFUNCTIONAL MATERIALS XIII}, author={Miles, Paul R. and Pash, Graham T. and Smith, Ralph C. and Oates, William S.}, year={2019} }
 @article{gao_miles_moura_hussaini_oates_2019, title={Uncertainty analysis of dielectric elastomer membranes under electromechanical loading}, volume={28}, ISSN={["1361-665X"]}, DOI={10.1088/1361-665X/aaedea}, abstractNote={The uncertainty in modeling finite deformation membrane electromechanics is analyzed by comparing low and high fidelity models against data on the dielectric elastomer VHB 4910. Both models include electrically and mechanically induced stress during transverse deformation of the membranes. The low fidelity model approximates deformation to be homogeneous while the high fidelity model includes a more accurate kinematic assumption of inhomogeneous deformation. We illustrate the importance of model fidelity with regards to parameter uncertainty and the associated propagation of errors in predicting membrane forces and charges in realistic actuator configurations. Both the low and high fidelity models are shown to accurately predict membrane forces and charges under different applied displacements and voltages. However, there are significant differences in the estimation of the dielectric constant used to model the membrane electromechanics. Bayesian statistics are used to quantify the uncertainty of the modeling approaches in light of both force–displacement and charge–voltage measurements. We quantify the hyperelastic, electromechanical coupling, and dielectric model uncertainties self-consistently using all mechanical and electrical experiments conducted on the 3M elastomer VHB 4910. We conclude that the low fidelity model is useful for system dynamic and control applications yet is limited in self-consistent predictions of both forces and charges from applied displacements and voltages. In comparison, the high fidelity model provides a more accurate description of the electromechanical coupling and dielectric constitutive behavior, but requires more computational power due to finite element discretization. In addition, the high fidelity modeling illustrates that a deformation dependent dielectric constant is necessary to self-consistently simulate both force–displacement and charge–voltage data.}, number={5}, journal={SMART MATERIALS AND STRUCTURES}, author={Gao, W. and Miles, P. R. and Moura, A. G. and Hussaini, M. Y. and Oates, W. S.}, year={2019}, month={May} }
 @inproceedings{hu_smith_burch_hays_oates_2013, title={Homogenized energy model and markov chain Monte Carlo simulations for macro fiber composites operating in broadband regimes}, booktitle={Proceedings of the ASME Conference on Smart Materials, Adaptive Structures and Intelligent Systems, vol 1}, author={Hu, Z. Z. and Smith, R. C. and Burch, N. and Hays, M. and Oates, W. S.}, year={2013}, pages={321–327} }
 @article{oates_zrostlik_eichhorn_smith_2010, title={A Non-linear Optimal Control Design using Narrowband Perturbation Feedback for Magnetostrictive Actuators}, volume={21}, ISSN={["1530-8138"]}, DOI={10.1177/1045389x10386398}, abstractNote={Non-linear optimal and narrowband feedback control designs are developed and experimentally implemented on a magnetostrictive Terfenol-D actuator. The non-linear optimal control design incorporates a non-linear and hysteretic ferromagnetic homogenized energy model within an optimal control formulation to reduce displacement tracking errors and increase bandwidth. Improvements in robustness in the steady-state regime are achieved by utilizing narrowband feedback. A narrowband filter is implemented by treating the nonlinear and hysteretic magnetostrictive constitutive behavior as higher-order harmonic disturbances which are mitigated by tuning the narrowband filter to penalize these harmonics for displacement tracking control problems. The control designs are then combined into a hybrid optimal controller with perturbation narrowband feedback. Both transient and steady-state tracking control is assessed to illustrate performance attributes in different operating regimes. Narrowband perturbation feedback is shown to mitigate errors in the steady-state operating regime, while non-linear optimal control provides enhanced tracking control in the transient regime. The hybrid control design is relevant to a broad number of smart material actuators that exhibit non-linear and hysteretic field-coupled constitutive behavior.}, number={16}, journal={JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES}, author={Oates, William S. and Zrostlik, Rick and Eichhorn, Scott and Smith, Ralph}, year={2010}, month={Nov}, pages={1681–1693} }
 @article{oates_smith_2009, title={Optimal Tracking Using Magnetostrictive Actuators Operating in Nonlinear and Hysteretic Regimes}, volume={131}, ISSN={["0022-0434"]}, DOI={10.1115/1.3072093}, abstractNote={Abstract : MANY ACTIVE MATERIALS EXHIBIT NONLINEARITIES AND HYSTERESIS WHEN DRIVEN AT FIELD LEVELS NECESSARY TO MEET STRINGENT PERFORMANCE CRITERIA IN HIGH PERFORMANCE APPLICATIONS. This often requires nonlinear control designs to effectively compensate for the nonlinear, hysteretic field-coupled material behavior. In this paper, an optimal control design is developed to accurately track a reference signal using magnetostrictive transducers. The methodology can be directly extended to transducers employing piezoelectric materials or shape memory alloys (SMAs) due to the unified nature of the constitutive model employed in the control design. The constitutive model is based on a framework that combines energy analysis at lattice length scales with stochastic homogenizations techniques to predict macroscopic material behavior. The constitutive model is incorporated into a finite element representation of the magnetostrictive transducer which provides the framework for developing the finite-dimensional nonlinear control design. The control design includes an open loop nonlinear component computed off-line with perturbation feedback around the optimal state trajectory. Estimation of unmeasurable states is achieved using a Kalman filter. The hybrid control technique provides the potential for real-time control implementation while providing robustness with regard to operating uncertainties and unmodeled dynamics.}, number={3}, journal={JOURNAL OF DYNAMIC SYSTEMS MEASUREMENT AND CONTROL-TRANSACTIONS OF THE ASME}, author={Oates, William S. and Smith, Ralph C.}, year={2009}, month={May} }
 @article{oates_smith_2008, title={Nonlinear optimal control techniques for vibration attenuation using magnetostrictive actuators}, volume={19}, ISSN={["1530-8138"]}, DOI={10.1177/1045389X06074159}, abstractNote={This article addresses the development of a nonlinear control design for attenuating structural vibrations using magnetostrictive transducers operating in nonlinear and highly hysteretic operating regimes. We consider as a prototype a thin plate subjected to exogenous pressure waves and controlled via Terfenol-D transducers at the plate edges; however, the methodology is sufficiently general to encompass a wide range of structures and magnetic transducer designs. Hysteresis inherent to the transducer materials is quantified using a homogenized energy framework and the resulting nonlinear constitutive relations are used to construct a PDE representation and corresponding finite dimensional model of the structural system. We employ optimal control theory to construct nonlinear open loop control inputs which accommodate the hysteresis inherent to the transducers but are not robust with regard to unmodeled dynamics or disturbances. Robustness is incorporated by employing perturbation techniques to provide linear feedback laws acting on measured disturbances. As illustrated via numerical examples, the resulting hybrid control design provides excellent control authority and robustness for transducers operating in hysteretic and nonlinear regimes.}, number={2}, journal={JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES}, author={Oates, William S. and Smith, Ralph C.}, year={2008}, month={Feb}, pages={193–209} }
 @article{westrain_oates_lupascu_roedel_lynch_2007, title={Mechanism of electric fatigue crack growth in lead zirconate titanate}, volume={55}, ISSN={["1873-2453"]}, DOI={10.1016/j.actamat.2006.08.029}, abstractNote={A series of experiments was performed with through-thickness cracks in ferroelectric double cantilever beam (DCB) specimens. Cyclic electric fields of different amplitudes were applied which resulted in cyclic crack propagation perpendicular to the electric field direction. Crack propagation was observed optically and three regimes were identified: a pop-in from a notch, steady-state crack growth and a decrease of the crack growth rate with increasing cycle number. Crack growth only occurred if the applied field exceeded the coercive field strength of the material. Furthermore, the crack extended during each field reversal and the crack growth rate increased with increasing field. Based on the experimental observations, a mechanistic understanding was developed and contrasted with a nonlinear finite element analysis which quantified the stress intensity in the DCB specimens. The driving forces for crack formation at the notch and subsequent fatigue crack growth were computed based on the distribution of residual stresses due to ferroelectric switching. The finite element results are in good agreement with the experimental observations and support the proposed mechanism.}, number={1}, journal={ACTA MATERIALIA}, author={Westrain, Ilona and Oates, William S. and Lupascu, Doru C. and Roedel, Juergen and Lynch, Christopher S.}, year={2007}, month={Jan}, pages={301–312} }
 @article{oates_2005, title={Heterogeneity influence on electric field induced piezoelectric microfracture}, volume={16}, ISSN={["1530-8138"]}, DOI={10.1177/1045389X05054850}, abstractNote={ Spatial variations in piezoelectric material properties can influence localized residual stresses under electro-mechanical loading, which has been shown to contribute to microfractures (Jiang, Q., Subbarao, E.C. and Cross, L.E. 1994. ''Grain Size Dependence of Electric Fatigue Behavior of Hot Pressed PLZT Ferroelectric Ceramics,'' Acta Metall. Mater., 42(11):3687–3694; Lynch, C.S. 1998. ''Fracture of Ferroelectric and Relaxor Electro-ceramics: Influences of Electric Field,'' Acta Mater., 46(2):599–608; Wang, Z., Jiang, Q., White, G.S. and Richardson, A.K. 1998. ''Processing Flaws in PZT Transducer Rings,'' Smart Mater. Struct., 7:867–873). The effect of residual stress on piezoelectric microfracture has been modeled by introducing a crack at the edge of a piezoelectric elliptic inclusion with dissimilar piezoelectric matrix material properties. Piezoelectric weight functions were used to assess changes in intensity factors and energy release rates when an inclusion is present. The shape of the elliptic inclusion is shown to have an effect on local driving forces. Additionally, comparison of impermeable and permeable crack face boundary conditions illustrate the importance of applying the more 'physical' permeable conditions to achieve positive flaw-localized driving forces under electrical loading. }, number={9}, journal={JOURNAL OF INTELLIGENT MATERIAL SYSTEMS AND STRUCTURES}, author={Oates, WS}, year={2005}, month={Sep}, pages={733–741} }