Titlebook: Energetic Relaxation to Structured Deformations; A Multiscale Geometr José Matias,Marco Morandotti,David R. Owen Book 2023 The Editor(s) (i

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https://doi.org/10.1007/978-3-7091-6298-9s. In the first one, we introduce the function spaces of first-order structured deformations, we show how first-order structured deformations can be approximated in a suitable sense by simple deformations, and we show how, starting from an initial energy defined on simple deformations, it is possibl

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Muslimische Herausforderung in Deutschland,r structured deformations, we show how they can be approximated in a suitable sense by simple deformations, and we show how, starting from an initial energy defined on simple deformations, it is possible to relax it to assign an energy to a given second-order structured deformation. This relaxation

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https://doi.org/10.1007/978-3-7091-6298-9e, and integral representation formulae are proved by means of the blow-up method. In the second part of this chapter, we present some results showing how the general relaxation theory can be applied to certain specific problems.

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2731-7595 chniques for readers acquainted with the fieldThis book is the first organized collection of some results that have been obtained by the authors, their collaborators, and other researchers in the variational approach to structured deformations. It sets the basis and makes more accessible the theoret

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Dark into Light: A Sociological Navigation, measures of the degree to which a deformed continuum with microvoids occupies a prescribed region in space, while Sect. 5.2 details aspects of multiscale differential geometry that permit one to distinguish between standard notions of curvature at the macrolevel and a notion of curvature at a submacroscopic level, away from disarrangement sites.

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Energetic Relaxation to Second-Order Structured Deformations,energy defined on simple deformations, it is possible to relax it to assign an energy to a given second-order structured deformation. This relaxation process is carried out in the context of .-convergence, and integral representation formulae are proved by means of the blow-up method or by the global method for relaxation (see Sect. .).

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Outlook for Future Research, measures of the degree to which a deformed continuum with microvoids occupies a prescribed region in space, while Sect. 5.2 details aspects of multiscale differential geometry that permit one to distinguish between standard notions of curvature at the macrolevel and a notion of curvature at a submacroscopic level, away from disarrangement sites.