Second-order structured deformations: relaxation, integral representation and applications
arXiv:1607.02311 · doi:10.1007/s00205-017-1120-5
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.
35 pages, Preprint SISSA: 37/MATE/2016