KLUEDO RSS Feed
KLUEDO Dokumente/documents
https://kluedo.ub.unikl.de/index/index/
Mon, 04 Mar 2019 14:30:05 +0100
Mon, 04 Mar 2019 14:30:05 +0100

Mathematical Modeling and Numerical Simulation of Magnetoelastic Coupling
https://kluedo.ub.unikl.de/frontdoor/index/index/docId/5519
Magnetoelastic coupling describes the mutual dependence of the elastic and magnetic fields and can be observed in certain types of materials, among which are the socalled "magnetostrictive materials". They belong to the large class of "smart materials", which change their shape, dimensions or material properties under the influence of an external field. The mechanical strain or deformation a material experiences due to an externally applied magnetic field is referred to as magnetostriction; the reciprocal effect, i.e. the change of the magnetization of a body subjected to mechanical stress is called inverse magnetostriction. The coupling of mechanical and electromagnetic fields is particularly observed in "giant magnetostrictive materials", alloys of ferromagnetic materials that can exhibit several thousand times greater magnitudes of magnetostriction (measured as the ratio of the change in length of the material to its original length) than the common magnetostrictive materials. These materials have wide applications areas: They are used as variablestiffness devices, as sensors and actuators in mechanical systems or as artificial muscles. Possible application fields also include robotics, vibration control, hydraulics and sonar systems.
Although the computational treatment of coupled problems has seen great advances over the last decade, the underlying problem structure is often not fully understood nor taken into account when using black box simulation codes. A thorough analysis of the properties of coupled systems is thus an important task.
The thesis focuses on the mathematical modeling and analysis of the coupling effects in magnetostrictive materials. Under the assumption of linear and reversible material behavior with no magnetic hysteresis effects, a coupled magnetoelastic problem is set up using two different approaches: the magnetic scalar potential and vector potential formulations. On the basis of a minimum energy principle, a system of partial differential equations is derived and analyzed for both approaches. While the scalar potential model involves only stationary elastic and magnetic fields, the model using the magnetic vector potential accounts for different settings such as the eddy current approximation or the full Maxwell system in the frequency domain.
The distinctive feature of this work is the analysis of the obtained coupled magnetoelastic problems with regard to their structure, strong and weak formulations, the corresponding function spaces and the existence and uniqueness of the solutions. We show that the model based on the magnetic scalar potential constitutes a coupled saddle point problem with a penalty term. The main focus in proving the unique solvability of this problem lies on the verification of an infsup condition in the continuous and discrete cases. Furthermore, we discuss the impact of the reformulation of the coupled constitutive equations on the structure of the coupled problem and show that in contrast to the scalar potential approach, the vector potential formulation yields a symmetric system of PDEs. The dependence of the problem structure on the chosen formulation of the constitutive equations arises from the distinction of the energy and coenergy terms in the Lagrangian of the system. While certain combinations of the elastic and magnetic variables lead to a coupled magnetoelastic energy function yielding a symmetric problem, the use of their dual variables results in a coupled coenergy function for which a mixed problem is obtained.
The presented models are supplemented with numerical simulations carried out with MATLAB for different examples including a 1D EulerBernoulli beam under magnetic influence and a 2D magnetostrictive plate in the state of plane stress. The simulations are based on material data of TerfenolD, a giant magnetostrictive materials used in many industrial applications.
ManĂ© Harutyunyan
doctoralthesis
https://kluedo.ub.unikl.de/frontdoor/index/index/docId/5519
Mon, 04 Mar 2019 14:30:05 +0100