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

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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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Authors and Affiliations

  1. Departamento de Matemática and CMAF-CIO, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, Edifício C6 Piso 1, 1749-016, Lisbon, Portugal

    Ana Cristina Barroso

  2. Departamento de Matemática, Instituto Superior Técnico, Av. Rovisco Pais, 1, 1049-001, Lisbon, Portugal

    José Matias

  3. Fakultät für Mathematik, Technische Universtität München, Boltzmannstrasse, 3, 85748, Garching, Germany

    Marco Morandotti

  4. Department of Mathematical Sciences, Carnegie Mellon University, 5000 Forbes Ave., Pittsburgh, PA, 15213, USA

    David R. Owen

Authors
  1. Ana Cristina Barroso
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  2. José Matias
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  3. Marco Morandotti
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  4. David R. Owen
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Corresponding author

Correspondence to Marco Morandotti.

Additional information

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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  • DOI: https://doi.org/10.1007/s00205-017-1120-5

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