A thermodynamically consistent model of magneto-elastic materials under diffusion at large strains and its analysis

0498635 - ÚT 2019 RIV CH eng J - Journal Article
Roubíček, Tomáš - Tomasetti, G.
A thermodynamically consistent model of magneto-elastic materials under diffusion at large strains and its analysis.
Zeitschrift für angewandte Mathematik und Physik. Roč. 69, č. 3 (2018), č. článku 55. ISSN 0044-2275. E-ISSN 1420-9039
R&D Projects: GA ČR(CZ) GA16-03823S
Institutional support: RVO:61388998
Keywords : elastic magnets * large strains * viscous Cahn-Hilliard equation * heat transfer * weak solutions * existence
OECD category: Applied mathematics
Impact factor: 1.618, year: 2018
https://link.springer.com/epdf/10.1007/s00033-018-0932-y?author_access_token=QJKDVLKeOPy6oNtYMfoiMPe4RwlQNchNByi7wbcMAY4688VdgGjuWyvcysZe14NAGutQK9B5nqkDNiVRo2NTsS9vj7-POvPFNcHlqG8-T_W2sssmX4_nT0crxkVwl8HfjGA0u7OoC8iT3GVxTU8ySw%3D%3D

A theory of elastic magnets is formulated under possible diffusion and heat flow governed by Fick’s and Fourier’slaws in the deformed configuration, respectively. The concepts of nonlocal nonsimple materials and viscous Cahn–Hilliard equations are used. The formulation of the problem uses Lagrangian configuration while the transport processes are pulled back. Except the static problem, the demagnetizing energy is ignored and only local non-selfpenetration is considered. The analysis as far as existence of weak solutions of the (thermo) dynamical problem is performed by a careful regularization and approximation by a Galerkin method, suggesting also a numerical strategy. Either ignoring or combining particular aspects, the model has numerous applications as ferro-to-paramagnetic transformation in elastic ferromagnets, diffusion of solvents in polymers possibly accompanied by magnetic effects (magnetic gels), or metal-hydride phase transformation in some intermetallics under diffusion of hydrogen accompanied possibly by magnetic effects, all in the full thermodynamical context under large strains.
Permanent Link: http://hdl.handle.net/11104/0291606