Existence results for incompressible magnetoelasticity

Martin Kružík; Ulisse Stefanelli; Jan Zeman

doi:10.3934/dcds.2015.35.2615

Article Contents

2015, Volume 35, Issue 6: 2615-2623. Doi: 10.3934/dcds.2015.35.2615

This issue Previous Article On the representation of hysteresis operators acting on vector-valued, left-continuous and piecewise monotaffine and continuous functions Next Article Control of crack propagation by shape-topological optimization

Existence results for incompressible magnetoelasticity

1.
Institute of Information Theory and Automation, Academy of Sciences of the Czech Republic, Pod vodárenskou věží 4, CZ-182 08 Praha 8
2.
Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, A-1090 Vienna
3.
Faculty of Civil Engineering, Czech Technical University, Thákurova 7, CZ-166 29 Praha 6

Received: November 2013

Revised: April 2014

Published: May 2017

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Abstract

We investigate a variational theory for magnetoelastic solids under the incompressibility constraint. The state of the system is described by deformation and magnetization. While the former is classically related to the reference configuration, magnetization is defined in the deformed configuration instead. We discuss the existence of energy minimizers without relying on higher-order deformation gradient terms. Then, by introducing a suitable positively $1$-homogeneous dissipation, a quasistatic evolution model is proposed and analyzed within the frame of energetic solvability.

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Mathematics Subject Classification: Primary: 74F15, 74K35; Secondary: 35Q74.

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