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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Alberti, G.: J. Funct. Anal. 100, 110–118 (1991)
Ambrosio, L., Fusco, N., Pallara, D.: OUP, (2000). ISBN: 9780198502456
Baía, M., Matias, J., Santos, P.M.: Proc. Royal Soc. Edinb. 142A, 239–271 (2012)
Barroso, A.C., Matias, J., Morandotti, M., Owen, D.R.: Math. Mech. Complex Syst. 5(2), 163–189 (2017)
Barroso, A.C., Matias, J., Morandotti, M., Owen, D.R.: Arch. Rational Mech. Anal. 225(3), 1025–1072 (2017)
Carita, G., Matias, J., Morandotti, M., Owen, D.R.: Dimension reduction in the context of structured deformations (2017). arXiv: 1709.02869
Choksi, R., Del Piero, G., Fonseca, I., Owen, D.R.: Math. Mech. Solids. 4, 321–356 (1999)
Choksi, R., Fonseca, I.: Arch. Rational Mech. Anal. 138, 37–103 (1997)
Ciblak, N., Lipkin, H.: In: Proceedings of DETC’98, Atlanta, Georgia Sep 13–16 (1998)
Del Piero, G., Owen, D.R.: Arch. Ration. Mech. Anal. 124, 99–155 (1993)
Del Piero, G., Truskinovsky, L.: Int. J. Solids Struct. 38, 1135–1148 (2001)
Deseri, L., Owen, D.R.: J. Elast. 70, 197–236 (2003)
Deseri, L., Owen, D.R.: Int. J. Eng. Sci. 96, 111–140 (2015)
Fonseca, I., Leoni, G.: Springer, New York, (2007). ISBN 978-0-387-69006-3
Fonseca, I., Müller, S.: Arch. Ration. Mech. Anal. 123, 1–49 (1993)
Matias, J., Morandotti, M., Zappale, E.: J. Math. Anal. Appl. 449, 1094–1132 (2017)
Matias, J., Santos, P.M.: Appl. Math. Optim. 69, 459–485 (2014)
Owen, D.R.: J. Elasticity 127(1), 115–150 (2017)
Owen, D.R., Paroni, R.: Arch. Ration. Mech. Anal. 155, 215–235 (2000)
Owen, D.R., Paroni, R.: Arch. Ration. Mech. Anal. 218, 1633–1652 (2015)
Paroni, R.: In: Del Piero, G., Owen, D.R. (eds.) CISM. vol. 447, Springer (2004)
Šilhavý, M.: Math. Mech. Complex Syst. 3, 83–100 (2015)
Šilhavý, M.: Math. Mech. Complex Syst. 5(2), 191–215 (2017)
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.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Morandotti, M. (2018). Structured Deformations of Continua: Theory and Applications. In: van Meurs, P., Kimura, M., Notsu, H. (eds) Mathematical Analysis of Continuum Mechanics and Industrial Applications II. CoMFoS 2016. Mathematics for Industry, vol 30. Springer, Singapore. https://doi.org/10.1007/978-981-10-6283-4_11
Download citation
DOI: https://doi.org/10.1007/978-981-10-6283-4_11
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-10-6282-7
Online ISBN: 978-981-10-6283-4
eBook Packages: EngineeringEngineering (R0)