Abstract
In this chapter we present and discuss the variational theory of second-order structured deformations. We introduce the function spaces of second-order 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 process is carried out in the context of Γ-convergence, and integral representation formulae are proved by means of the blow-up method or by the global method for relaxation (see Sect. 2.4).
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Matias, J., Morandotti, M., Owen, D.R. (2023). Energetic Relaxation to Second-Order Structured Deformations. In: Energetic Relaxation to Structured Deformations. SpringerBriefs on PDEs and Data Science. Springer, Singapore. https://doi.org/10.1007/978-981-19-8800-4_4
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DOI: https://doi.org/10.1007/978-981-19-8800-4_4
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