We reconsider the derivation of plate theories as Γ-limits of 3-dimensional nonlinear elasticity and define a suitable notion for the interpenetration of matter in the limit configuration. This isdone via the Brouwer degree. For the approximating maps, we adopt as definition of interpenetrationof matter the notion of non-invertibility almost everywhere, see [J.M. Ball, Proc. Roy. Soc. EdinburghSect. A 88 (1981) 315–328]. Given a limit map satisfying the former interpenetration property, we showthat any recovery sequence (in the sense of Γ-convergence) has to consist of maps that satisfy the latterinterpenetration property except for finitely many sequence elements. Then we explain how our resultis applied in the context of the derivation of plate theories.
INTERPENETRATION OF MATTER IN PLATE THEORIES OBTAINED AS Γ-LIMITS
Runa E
2017-01-01
Abstract
We reconsider the derivation of plate theories as Γ-limits of 3-dimensional nonlinear elasticity and define a suitable notion for the interpenetration of matter in the limit configuration. This isdone via the Brouwer degree. For the approximating maps, we adopt as definition of interpenetrationof matter the notion of non-invertibility almost everywhere, see [J.M. Ball, Proc. Roy. Soc. EdinburghSect. A 88 (1981) 315–328]. Given a limit map satisfying the former interpenetration property, we showthat any recovery sequence (in the sense of Γ-convergence) has to consist of maps that satisfy the latterinterpenetration property except for finitely many sequence elements. Then we explain how our resultis applied in the context of the derivation of plate theories.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
