Inserted: 8 jul 2016
Last Updated: 19 jul 2017
Journal: Arch. Rational Mech. Anal.
Preprint SISSA: 37$/$MATE$/$2016
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.