No abstract

This paper provides a theory for quantifying the hysteresis and constitutive nonlinearities inherent to piezoceramic compounds through a combination of free energy analysis and stochastic homogenization techniques. In the first step of the model development, Helmholtz and Gibbs free energy relations are constructed at the lattice or domain level to quantify the relation between the field and polarization in homogeneous, single crystal compounds which exhibit uniform effective fields. The effects of material nonhomogeneities, polycrystallinity, and variable effective fields are subsequently incorporated through the assumption that certain physical parameters, including the local coercive and effective fields, are randomly distributed and hence manifestations of stochastic density functions associated with the material. Stochastic homogenization in this manner provides low-order macroscopic models with effective parameters that can be correlated with physical properties of the data. This facilitates the identification of parameters for model construction, model updating to accommodate changing operating conditions, and control design utilizing model-based inverse compensators. Attributes of the model, including the guaranteed closure of biased minor loops in quasistatic drive regimes, are illustrated through examples.i Report Documentation PageForm Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number.

Thin-film shape memory alloys (SMAs) have become excellent candidates for microactuator fabrication in MEMS. We develop a material model based on a combination of free energy principles in combination with stochastic homogenization techniques. In the first step of the development, we construct free energies and develop phase fraction and thermal evolution laws for homogeneous, single-crystal SMAs. Second, we extend the single-crystal model to accommodate material inhomogeneities and polycrystalline compounds. The combined model predicts rate-dependent, uniaxial SMA deformations due to applied stress and temperature. Moreover, the model admits a low-order formulation that is suitable for subsequent control design. We illustrate aspects of the model through comparison with thin-film NiTi superelastic hysteresis data.

This paper addresses the modeling of hysteresis in ferroelectric materials through consideration of domain wall bending and translation. The development is considered in two steps. In the rst step, dielectric constitutive relations are obtained through consideration of Langevin, Ising spin and preferred orientation theory with domain interactions incorporated through mean eld relations. This yields a model for the anhysteretic polarization that occurs in the absence of domain wall pinning. In the second step, hysteresis is incorporated through the consideration of domain wall dynamics and the quanti cation of energy losses due to inherent inclusions or pinning sites within the material. This yields a model analogous to that developed by Jiles and Atherton for ferromagnetic materials. The viability of the model is illustrated through comparison with experimental data from a PMN-PT-BT actuator operating at a temperature within the ferroelectric regime.

This paper addresses the modeling of hysteresis and nonlinear constitutive relations in piezoelectric materials at moderate to high drive levels. Hysteresis and nonlinearities are due to the domain structure inherent to the materials and both aspects must be addressed to attain the full potential of the materials as sensors and actuators in high performance applications. The model employed here is based on previously developed theory for hysteresis in general ferroelectric materials. This theory is based on the quantification of the reversible and irreversible motion of domain walls pinned at inclusions in the material. This yields an ordinary differential equation (ODE) model having five parameters. The relationship of the parameters to physical attributes of the materials is detailed and algorithms for determining estimates of the parameters using measured values of the coercive field, differential susceptibility and saturation properties of the materials are detailed. The accuracy of the model and its capability for the prediction of measured polarization at various drive levels is illustrated through a comparison with experimental data from PZT5A, PZT5H and PZT4 compounds. Finally, the ODE model formulation is amenable to inversion which facilitates the construction of an inverse compensator for linear control design.