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Structured Deformations of Continua: Theory and Applications

  • Marco Morandotti
Conference paper
Part of the Mathematics for Industry book series (MFI, volume 30)

Abstract

The scope of this contribution is to present an overview of the theory of structured deformations of continua, together with some applications. Structured deformations aim at being a unified theory in which elastic and plastic behaviours, as well as fractures and defects can be described in a single setting. Since its introduction in the scientific community of rational mechanicists [10], the theory has been put in the framework of variational calculus [8], thus allowing for solution of problems via energy minimization. Some background, three problems and a discussion on future directions are presented.

Notes

Acknowledgements

The author acknowledges partial support for this research from the following grants: FCT\(\_\)UTA/CMU/MAT/0005/2009 of the Fundação para a Ciência e a Tecnologia through the Carnegie Mellon Portugal Program; ERC Advanced grant Quasistatic and Dynamic Evolution Problems in Plasticity and Fracture (Grant agreement 290888); INdAM-GNAMPA project 2015 Fenomeni Critici nella Meccanica dei Materiali: un Approccio Variazionale; ERC Starting grant High-Dimensional Sparse Optimal Control (Grant agreement 306274). The author is a member of the GNAMPA group of INdAM. The author is grateful to J. Matias and D. R. Owen for valuable suggestions in writing this note.

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Copyright information

© Springer Nature Singapore Pte Ltd. 2018

Authors and Affiliations

  1. 1.Technische Universität MünchenGarchingGermany

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