A Unified Model for Hysteresis in Ferroic Materials
- PDF / 188,032 Bytes
- 12 Pages / 612 x 792 pts (letter) Page_size
- 56 Downloads / 217 Views
W5.9.1
A Uni ed Model for Hysteresis in Ferroic Materials Stefan Seelecke1 and Ralph C. Smith Center for Research in Scienti c Computation, North Carolina State Univ., Raleigh, NC 27695 1 Dept. Mech. & Aero. Eng. Center for Research in Scienti c Computation, North Carolina State Univ., Raleigh, NC 27695 ABSTRACT This paper provides a uni ed modeling framework for ferroelectric, ferromagnetic and ferroelastic materials operating in hysteretic and nonlinear regimes. Whereas the physical mechanisms which produce hysteresis and constitutive nonlinearities in these materials differ at the microscopic level, shared energy relations can be derived at the lattice, or mesoscopic, scale. This yields a class of models which are appropriate for homogeneous, single crystal compounds. Stochastic homogenization techniques are then employed to construct macroscopic models suitable for nonhomogeneous, polycrystalline compounds with variable effective elds or stresses. This uni ed methodology for quantifying hysteresis and constitutive nonlinearities for a broad class of ferroic compounds facilitates both material characterization and subsequent model-based control design. Attributes of the models are illustrated through comparison with piezoceramic, magnetostrictive and thin lm SMA data. Keywords: Uni ed free energy models, hysteresis, constitutive nonlinearities, ferroic materials INTRODUCTION Hysteresis and constitutive nonlinearities are an inherent property of ferroelectric, ferromagnetic and ferroelastic compounds under a wide range of operating frequencies and drive regimes. For certain applications, these nonlinear effects can be minimized through low drive operation or feedback mechanisms. In other cases, however, hysteresis and nonlinear dynamics are unavoidable and must be accommodated for accurate material characterization and subsequent model-based control design. For example, hysteresis inherent to the piezoceramic nanopositioning elements employed in all present atomic force microscope (AFM) designs can be mitigated at low frequencies through PID or robust feedback control laws [4, 5, 13]. However, at the high scan rates required for real-time product diagnostics or monitoring cellular processes, noise to signal ratios preclude the sole use of feedback control laws to mitigate hysteresis, and control designs utilizing model-based inverse compensators are under investigation [18]. Furthermore, for many applications utilizing SMA, maximal hysteresis is desired to optimize damping since energy dissipation is proportional to the area of the hysteresis loop. Hence, for civil applications in which SMA tendons are utilized to attenuate earthquake vibrations in buildings, operation in highly hysteretic pseudoelastic regimes is required. This necessitates the development of uni ed models which characterize hysteresis and constitutive nonlinearities in a manner which facilitates subsequent transducer design and model-based control implementation.
W5.9.2
In this paper, we construct a hierarchy of uni ed models based on energy
Data Loading...
