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Dimension reduction in the context of structured deformations

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Dimension reduction in the context of structured deformations
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26
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The theory of structured deformations shows good potential to deal with mechanical problems where multiple scales and fractures are present. Mathematically, it amounts to relaxing a given energy functional and to show also the relaxed one has an integral representation. In this seminar, I will focus on a problem for thin objects: the derivation of a 2D relaxed energy via dimension reduction from a 3D energy, incorporating structured deformations in the relaxation procedure. I will discuss the two-step relaxation (first dimension reduction, then structured deformations and viceversa) and I will compare it with another result in which the two relaxation procedures are carried out simultaneously. An explicit example for purely interfacial initial energies will complete the presentation.