×

A three-dimensional phenomenological model for magnetic shape memory alloys. (English) Zbl 1279.74026

Summary: We present a three-dimensional thermodynamically-consistent phenomenological model for the magneto-mechanical behavior of magnetic shape memory materials featuring a cubic-to-tetragonal martensitic transformation. The existence of energetic solutions for both the constitutive relation problem and the three-dimensional quasi-static evolution problem is proved. The proposed model reduces to some former one via parameter asymptotics by means of a rigorous \(\Gamma \)-convergence argument.

MSC:

74M05 Control, switches and devices (“smart materials”) in solid mechanics
74F15 Electromagnetic effects in solid mechanics
74H20 Existence of solutions of dynamical problems in solid mechanics
35Q74 PDEs in connection with mechanics of deformable solids
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Auricchio, Improvements and algorithmical considerations on a recent threedimensional model describing stress-induced solid phase transformations, Internat. J. Numer. Methods Engrg. 55 pp 1255– (2002) · Zbl 1062.74580 · doi:10.1002/nme.619
[2] Auricchio, A three-dimensional model describing stress-temperature induced solid phase transformations. Part II: thermomechanical coupling and hybrid composite applications, Internat. J. Numer. Methods Engrg. 61 pp 716– (2004) · Zbl 1075.74598 · doi:10.1002/nme.1087
[3] A.-L. Bessoud U. Stefanelli Magnetic Shape Memory Alloys: three-dimensional modeling and analysis, Math.Models Methods Appl. Sci. , to appear (2010).
[4] Hirsinger, Internal variable model for magneto-mechanical behaviour of ferromagnetic shape memory alloys Ni-Mn-Ga, J. Phys. IV 112 pp 977–
[5] Kiefer, Modeling the coupled strain and magnetization response of magnetic shape memory alloys under magnetomechanical loading, J. Intell. Mater. Syst. Struct. 20 pp 143– (2009) · doi:10.1177/1045389X07086688
[6] A. Mielke Evolution of rate-independent systems , in: Evolutionary Equations Vol. II, edited by C. M. Dafermos and E. Feireisl, Handbook of Differential Equations. (Elsevier/North-Holland, Amsterdam, 2005), chap. 6.
[7] Mielke, {\(\Gamma\)}-imits and relaxations for rate-independent evolutionary problems, Calc. Var. Partial Differential Equations 31 (3) pp 387– (2008) · Zbl 1302.49013 · doi:10.1007/s00526-007-0119-4
[8] Souza, Three-dimensional model for solids undergoing stressinduces transformations, Eur. J. Mech. A Solids 17 pp 789– (1998) · Zbl 0921.73024 · doi:10.1016/S0997-7538(98)80005-3
[9] Tickle, Magnetic and magnetomechanical properties of Ni2MnGa, J. Magn. Magn. Mater. 195 pp 627– (1999) · doi:10.1016/S0304-8853(99)00292-9
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.