Nonlocal Variational Problems in Nonlinear Electromagneto-Elastostatics
- 1 November 1988
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Mathematical Analysis
- Vol. 19 (6) , 1329-1347
- https://doi.org/10.1137/0519097
Abstract
The effects of arbitrary applied electric and magnetic fields on unshielded, nonlinear, deformable, polarizable, magnetizable, nonconducting bodies are studied. Both monotone materials (dielectric, paramagnetic, etc.) and classical ferromagnetic materials are considered. The lack of shielding forces us to consider unknown fields outside of the material. This leads to nonlocal (“shape-dependent”) effects. The work of Ball is extended [“Convexity conditions and existence theorems in nonlinear elasticity,” Arch. Rat. Mech. Anal., 63 (1977), pp. 337–403] to get an existence theory using direct methods of the calculus of variations.Keywords
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