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Phase Transformations in Electrically Conductive Ferromagnetic Shape-Memory Alloys, Their Thermodynamics and Analysis

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Abstract

We derive a thermodynamically consistent general continuum-mechanical model describing mutually coupled martensitic and ferro/paramagnetic phase transformations in electrically-conductive magnetostrictive materials such as NiMnGa. We use small-strain and eddy-current approximations, yet large velocities and electric current injected through the boundary are allowed. Fully nonlinear coupling of magneto-mechanical and thermal effects is considered. The existence of energy-preserving weak solutions is proved by showing convergence of time-discrete approximations constructed by a carefully designed semi-implicit regularized scheme.

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Authors and Affiliations

  1. Mathematical Institute, Charles University, Sokolovská 83, 186 75, Praha 8, Czech Republic

    Tomáš Roubíček

  2. Institute of Thermomechanics of the ASCR, Dolejškova 5, 182 00, Praha 8, Czech Republic

    Tomáš Roubíček

  3. Dipartimento di Ingegneria Civile, Universitá di Roma “Tor Vergata”, Via Politecnico 1, Rome, 00133, Italy

    Giuseppe Tomassetti

Authors
  1. Tomáš Roubíček
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  2. Giuseppe Tomassetti
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Correspondence to Tomáš Roubíček.

Additional information

Communicated by F. Otto

This work was supported by the Italian INdAM-GNFM, and also in part by the grants 201/09/0917, 201/10/0357, and 201/12/0671 (GA ČR), LC 06052 (MŠMT ČR), by the institutional support RVO: 61388998 (ČR), as well as the CENTEM project no. CZ.1.05/21.00/03.0088 (within OP RDI) at New technologies research centre (ZČU, Plzeň).

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Roubíček, T., Tomassetti, G. Phase Transformations in Electrically Conductive Ferromagnetic Shape-Memory Alloys, Their Thermodynamics and Analysis. Arch Rational Mech Anal 210, 1–43 (2013). https://doi.org/10.1007/s00205-013-0648-2

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  • DOI: https://doi.org/10.1007/s00205-013-0648-2

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