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1 Bulletin of the Polish Academy of Sciences. Technical Sciences

1 2013

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Incompressible limit for a magnetostrictive energy functional

Gambin B., Bielski W.

Bulletin of the Polish Academy of Sciences. Technical Sciences

2013

Vol. 61, nr 4

1025--1030

The modern materials undergoing large elastic deformations and exhibiting strong magnetostrictive effect are modelled here by free energy functionals for nonlinear and non-local magnetoelastic behaviour. The aim of this work is to prove a new theorem which claims that a sequence of free energy functionals of slightly compressible magnetostrictive materials with a non-local elastic behaviour, converges to an energy functional of a nearly incompressible magnetostrictive material. This convergence is referred to as a Γ -convergence. The non-locality is limited to non-local elastic behaviour which is modelled by a term containing the second gradient of deformation in the energy functional.