4 Title: Mathematical modeling of magnetostrictive materials Author: Lukáš Vermach Department: Mathematical Institute of Charles University Advisor: Priv.-Doz. Dr. habil. RNDr. Martin Kružík Ph.D., Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic Advisor's e-mail address: kruzik@utia.cas.cz Abstract In the present work we introduce an isotermic mathematical model of ferromagnetic shape memory alloys (FSMAs). FSMAs are a special class of magnetostrictive materials, i.e. materials which deform their shape on account of external magnetic field or which change magnetization as a consequence of strain. This property originates from phase transformations that occur within the material when being exposed to external loading. First, the stationary model of FSMA is formulated. The thermodynamical potential is composed (Helmholz free energy) and its non-quasiconvexity is discussed. The quasicon- vexification is performed via the relaxation theory, i.e. quasiconvex envelope construction. For such a model the existence theory is built. Then, taking advantage of the stationary case the evolutionary model is developed. The attention is drawn to hysteresis, which arises from energy dissipation. The time discretization leads to a sequence of hysteresis-modified stationary problems (the...
| Identifer | oai:union.ndltd.org:nusl.cz/oai:invenio.nusl.cz:313783 |
| Date | January 2011 |
| Creators | Vermach, Lukáš |
| Contributors | Kružík, Martin, Zeman, Jan |
| Source Sets | Czech ETDs |
| Language | English |
| Detected Language | English |
| Type | info:eu-repo/semantics/masterThesis |
| Rights | info:eu-repo/semantics/restrictedAccess |
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