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Journal Article

Existence Results for Incompressible Magnetoelasticity

Kružík Martin, Stefanelli U., Zeman J.

: Discrete and Continuous Dynamical Systems vol.35, 6 (2015), p. 2615-2623

: GA13-18652S, GA ČR

: magnetoelasticity, magnetostrictive solids, incompressibility, existence of minimizers, quasistatic evolution, energetic solution

: 10.3934/dcds.2015.35.2615

: http://library.utia.cas.cz/separaty/2015/MTR/kruzik-0443017.pdf

(eng): We investigate a variational theory for magnetoelastic solids un- der the incompressibility constraint. The state of the system is described by deformation and magnetization. While the former is classically related to the reference conguration, magnetization is dened in the deformed congura- tion instead. We discuss the existence of energy minimizers without relying on higher-order deformation gradient terms. Then, by introducing a suitable pos- itively 1-homogeneous dissipation, a quasistatic evolution model is proposed and analyzed within the frame of energetic solvability.

: BA