Calculus of Variations and Geometric Measure Theory
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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 12 May 2017


Accepted Paper

Inserted: 8 jul 2016
Last Updated: 12 may 2017

Journal: ARMA
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.


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