Published Paper

Inserted: 8 jul 2016
Last Updated: 19 jul 2017

Journal: Arch. Rational Mech. Anal.
Volume: 225
Pages: 1025-1072
Year: 2017
Doi: 10.1007/s00205-017-1120-5

Preprint SISSA: 37$/$MATE$/$2016

Abstract:

Second-order structured deformations of continua provide an extension of the multiscale geometry of first-order structured deformations by taking into account the effects of submacroscopic bending and curving. We derive here an integral representation for a relaxed energy functional in the setting of second-order structured deformations. Our derivation covers inhomogeneous initial energy densities (i.e., with explicit dependence on the position); finally, we provide explicit formulas for bulk relaxed energies as well as anticipated applications.

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