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- Technische Fakultät -ohne weitere Spezifikation- (4) (remove)

- Finite Element Formulation for Ferroelectric Hysteresis of Piezoelectric Materials (2010)
- For the numerical simulation of non-linear piezoelectric material behavior, we use a constitutive relation that is based on a decomposition of the physical quantities dielectric displacement and mechanical strain into a reversible and an irreversible part. Therein, we set the irreversible part of the dielectric displacement equal to the irreversible electric polarization and express the irreversible mechanical strain by a polynomial ansatz of the irreversible electric polarization. The reversible parts of mechanical strain and dielectric displacement are further described by the linear piezoelectric constitutive law. We apply a Preisach hysteresis operator to compute the irreversible polarization from the history of the driving electric field. Furthermore, the entries of the piezoelectric modulus tensor are assumed to be functions of the electric polarization. To efficiently solve the non-linear system of partial differential equations, we have developed a quasi-Newton scheme and use the finite element (FE) method for the numerical solution. This FE scheme has been applied to numerically calculate the dynamic behavior of a piezoelectric disc and a stack actuator. The obtained results compare well to measured data.

- Efficient Modeling of Ferroelectric Behavior for the Analysis of Piezoceramic Actuators (2008)
- This work proposes a method of efficiently modeling the hysteresis of ferroelectric materials. Our approach includes the additive combination of a reversible and an irreversible portion of the polarization and strain, respectively. Whereas the reversible parts correspond to the common piezoelectric linear equations, the irreversible parts are modeled by hysteresis operators. These operators are based on Preisach and Jiles-Atherton hysteresis models which are well-established tools in ferromagnetic modeling. In contrast to micromechanical approaches, a Preisach or a Jiles-Atherton hysteresis operator can be efficiently numerically evaluated. A comparison of the resulting simulations to measured data concludes the article.

- Iterative identification of hysteresis in Maxwell's equations (2007)
- Purpose – In a model resulting from Maxwell's equations with a constitutive law using Preisach operators for incorporating magnetization hysteresis, this paper aims at identifying the hysteresis operator, i.e. the Preisach weight function, from indirect measurements. Design/methodology/approach – Dealing with a nonlinear inverse problem, one has to apply iterative methods for its numerical solution. For this purpose several approaches are proposed based on fixed point or Newton type ideas. In the latter case, one has to take into account nondifferentiability of the hysteresis operator. This is done by using differentiable substitutes or quasi-Newton methods. Findings – Numerical tests with synthetic data show that fixed point methods based on fitting after a full forward sweep (alternating iteration) and Newton type iterations using the hysteresis centerline or commutation curve exhibit a satisfactory convergence behavior, while fixed point iterations based on subdividing the time interval (Kaczmarz) suffer from instability problems and quasi Newton iterations (Broyden) are too slow in some cases. Research limitations/implications – Application of the proposed methods to measured data will be the subject of future research work. Practical implications – The proposed methodologies allow to determine material parameters in hysteresis models from indirect measurements. Originality/value – Taking into account the full PDE model, one can expect to get accurate and reliable results in this model identification problem. Especially the use of Newton type methods – taking into account nondifferentiability – is new in this context.

- PDE based determination of piezoelectric material tensors (2006)
- The exact numerical simulation of piezoelectric transducers requires the knowledge of all material tensors that occur in the piezoelectric constitutive relations. To account for mechanical, dielectric and piezoelectric losses, the material parameters are assumed to be complex. The issue of material tensor identification is formulated as an inverse problem: As input measured impedance values for different frequency points are used, the searched-for output is the complete set of material parameters. Hence, the forward operator F mapping from the set of parameters to the set of measurements, involves solutions of the system of partial differential equations arising from application of Newton's and Gauss' law to the piezoelectric constitutive relations. This, via two or three dimensional finite element discretisation, leads to an indefinite system of equations for solving the forward problem. Well-posedness of the infinite dimensional forward problem is proven and efficient solution strategies for its discretized version are presented. Since unique solvability of the inverse problem may hardly be verified, the system of equations we have to solve for recovering the material tensor entries can be rank deficient and therefore requires application of appropriate regularisation strategies. Consequently, inversion of the (nonlinear) parameter-to-measurement map F is performed using regularised versions of Newton's method. Numerical results for different piezoelectric specimens conclude this paper.