@article{hu_smith_stuebner_hays_oates_2011, title={Statistical Parameter Estimation for Macro Fiber Composite Actuators using the Homogenized Energy Model}, volume={7978}, ISSN={["0277-786X"]}, DOI={10.1117/12.884622}, abstractNote={Macro Fiber Composites (MFC) are planar actuators comprised of PZT fibers embedded in an epoxy matrix that is sandwiched between electrodes. Due to their construction, they exhibit significant durability and flexibility in addition to being lightweight and providing broadband inputs. They are presently being considered for a range of applications including positioning and control of membrane mirrors and configurable aerospace structures. However, they also exhibit hysteresis and constitutive nonlinearities that must be incorporated in models to achieve the full potential of the devices. In this paper, we discuss the development of a model that quantifies the hysteresis and constitutive nonlinearities in a manner that promotes subsequent control design. The constitutive model is constructed using the homogenized energy framework for ferroelectric hysteresis and used to develop resulting system models. The performance of the models is validated with experimental data.}, journal={BEHAVIOR AND MECHANICS OF MULTIFUNCTIONAL MATERIALS AND COMPOSITES 2011}, author={Hu, Zhengzheng and Smith, Ralph C. and Stuebner, Michael and Hays, Michael and Oates, William S.}, year={2011} }
 @article{stuebner_haider_2010, title={A fast quadrature-based numerical method for the continuous spectrum biphasic poroviscoelastic model of articular cartilage}, volume={43}, ISSN={0021-9290}, url={http://dx.doi.org/10.1016/j.jbiomech.2010.02.023}, DOI={10.1016/j.jbiomech.2010.02.023}, abstractNote={A new and efficient method for numerical solution of the continuous spectrum biphasic poroviscoelastic (BPVE) model of articular cartilage is presented. Development of the method is based on a composite Gauss-Legendre quadrature approximation of the continuous spectrum relaxation function that leads to an exponential series representation. The separability property of the exponential terms in the series is exploited to develop a numerical scheme that can be reduced to an update rule requiring retention of the strain history at only the previous time step. The cost of the resulting temporal discretization scheme is O(N) for N time steps. Application and calibration of the method is illustrated in the context of a finite difference solution of the one-dimensional confined compression BPVE stress-relaxation problem. Accuracy of the numerical method is demonstrated by comparison to a theoretical Laplace transform solution for a range of viscoelastic relaxation times that are representative of articular cartilage.}, number={9}, journal={Journal of Biomechanics}, publisher={Elsevier BV}, author={Stuebner, Michael and Haider, Mansoor A.}, year={2010}, month={Jun}, pages={1835–1839} }
 @article{stuebner_smith_2010, title={Inverse Model Construction for Control Implementation of Macro Fiber Composite Actuators Operating in Hysteretic Regimes}, volume={7644}, ISSN={["0277-786X"]}, DOI={10.1117/12.848256}, abstractNote={Macro Fiber Composite (MFC) actuators utilize PZT fibers embedded in an epoxy matrix for structural actuation. Due to their construction, they are lightweight and provide broadband inputs. Significant advantages of MFC actuators are their high performance, durability, and flexibility when compared to traditional piezoceramic actuators. They are presently being considered for a range of applications including positioning of membrane mirrors and structural control in the aerospace and automotive industry. However, they exhibit varying degrees of hysteresis and constitutive nonlinearities throughout their operating range that must be incorporated in models to achieve the full capabilities of the materials. In this paper, hysteresis is modeled using the homogenized energy model. The inverse model is then used to construct an inverse compensator framework suitable for subsequent control design. The performance of the inverse compensator is illustrated through a numerical example.}, journal={BEHAVIOR AND MECHANICS OF MULTIFUNCTIONAL MATERIALS AND COMPOSITES 2010}, author={Stuebner, Michael and Smith, Ralph C.}, year={2010} }
 @article{stuebner_atulasimha_smith_2009, title={Quantification of hysteresis and nonlinear effects on the frequency response of ferroelectric and ferromagnetic materials}, volume={18}, ISSN={["1361-665X"]}, DOI={10.1088/0964-1726/18/10/104019}, abstractNote={Ferroelectric (e.g., PZT and PMN) and ferromagnetic (e.g., Terfenol-D) materials exhibit high energy densities, broadband drive capabilities, and the capacity for both actuating and sensing. This makes them attractive as compact transducers for a wide range of applications. However, the materials also exhibit hysteresis and constitutive nonlinearities, at all drive levels, that must be quantified and accommodated to achieve stringent tracking requirements. Whereas considerable effort has been made on model development and understanding these materials in the parameter space and time domain, comprehensive quantification of these effects in the frequency domain is currently lacking. In this paper, we employ the homogenized energy model, in combination with thin beam theory, to quantify the frequency domain behavior of ferroelectric and ferromagnetic materials. This model combines energy analysis at the lattice level with stochastic homogenization techniques to provide a framework that effectively quantifies the effect of hysteresis, constitutive nonlinearities, bias fields and AC drive levels on the material dynamics in both the time and frequency domains. Aspects of the model are illustrated and validated through numerical and experimental examples.}, number={10}, journal={SMART MATERIALS AND STRUCTURES}, author={Stuebner, M. and Atulasimha, J. and Smith, R. C.}, year={2009}, month={Oct} }
 @article{babuska_lipton_stuebner_2008, title={The penetration function and its application to microscale problems}, volume={48}, ISSN={["1572-9125"]}, DOI={10.1007/s10543-008-0182-z}, number={2}, journal={BIT NUMERICAL MATHEMATICS}, author={Babuska, Ivo and Lipton, Robert and Stuebner, Michael}, year={2008}, month={Jun}, pages={167–187} }