Calculus of Variations and Geometric Measure Theory

A. C. Barroso - J. Matias - M. Morandotti - D. R. Owen

Second-order structured deformations: relaxation, integral representation and applications

created by morandott on 08 Jul 2016
modified on 19 Jul 2017


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

ArXiv: 1607.02311 PDF

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.