Archive for Rational Mechanics and Analysis

, Volume 225, Issue 3, pp 1025–1072 | Cite as

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

  • Ana Cristina Barroso
  • José Matias
  • Marco MorandottiEmail author
  • David R. Owen


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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© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Departamento de Matemática and CMAF-CIO, Faculdade de CiênciasUniversidade de LisboaLisbonPortugal
  2. 2.Departamento de MatemáticaInstituto Superior TécnicoLisbonPortugal
  3. 3.Fakultät für MathematikTechnische Universtität MünchenGarchingGermany
  4. 4.Department of Mathematical SciencesCarnegie Mellon UniversityPittsburghUSA

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