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Relationship between existence of energy minimizers of incompressible and nearly incompressible magnetostrictive materials. (English) Zbl 1237.74034

Summary: Models of incompressible and slightly compressible magnetostrictive materials are introduced. They are given by the free energy functionals which depend on magnetization and elastic deformation as well as on their gradients. We demonstrate the existence of minimum of an energy functional for a slightly compressible material. We also prove a theorem on convergence of a sequence of minimizers of less and less compressible material energy functionals to a minimizer of energy of incompressible material. Besides the existence of solution of the incompressible magnetostrictive problem is obtained.

MSC:

74G65 Energy minimization in equilibrium problems in solid mechanics
49J45 Methods involving semicontinuity and convergence; relaxation
74F15 Electromagnetic effects in solid mechanics
78A55 Technical applications of optics and electromagnetic theory
82D40 Statistical mechanics of magnetic materials
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