Mathematical Modeling of Magnetostrictive Materials

Mané Harutyunyan and Bernd Simeon, Felix-Klein-Center for Mathematics, University of Kaiserslautern

28 Apr 2014, 16:15; Location: S2|17/103, Schlossgartenstrasse 8

Magnetostrictive materials belong to the large class of Smart Materials, which change their mechanical behavior and properties in response to the application of an external field, such as temperatur or magnetic field. Particularly magnetostrictive elastomers, composites consisting of ferrous particles dispersed in an elastomeric matrix, can exhibit large deformations due to an externally apllied magnetic field. In the recent years, magnetostrictive materials have attracted considerable interests due to their wide application areas, e.g. as variable stiffness-devices and high-strain actuators in mechanical systems, artifical muscles as well as sensors or actuators in robotics.

From a mathematical point of view, the modeling of MS materials involves the strong (two-way) coupling of the magnetic and mechanical fields in the stationary case and an three-field-coupling with the electric field in the transient case. By talking additionally into account geometric and material nonlinearities, the modeling can become rather tedious and complicated. Thus, there is a clear need for reduces mathematical models, which provide better understanding of the complex phenomenon of coupling.

This talk is aimed at the description of the magneto-mechanical coupling using a simple model of an isotropic, ferromagnetic Euler-Bernoulli-beam. The main focus lies on the mathematical formulation of a coupled magneto-elastic problem by means of a PDE with appropriate boundary conditions. The numerical modeling is performed by using the Finite Element Method. Starting with linear material laws and the stationary case, the model is extended step by step, considering also material and geometric nonlinearities as well as time-dependent analysis. To confirm the theoretical results, corresponding simulations carried out with Matlab are presented.

Category: CE Seminar


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