Second-Order Structured Deformations: Relaxation, Integral Representation and Applications

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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Correspondence to Marco Morandotti.

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Communicated by E. G. Virga

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Barroso, A.C., Matias, J., Morandotti, M. et al. Second-Order Structured Deformations: Relaxation, Integral Representation and Applications. Arch Rational Mech Anal 225, 1025–1072 (2017). https://doi.org/10.1007/s00205-017-1120-5

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