Explicit integral representations of the relaxation of non-local energies for structured deformations
Duration: 42 mins 35 secs
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Description: |
Matias, J
Wednesday 19th June 2019 - 15:10 to 15:50 |
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Created: | 2019-06-26 14:28 |
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Collection: | The mathematical design of new materials |
Publisher: | Isaac Newton Institute |
Copyright: | Matias, J |
Language: | eng (English) |
Distribution: | World (downloadable) |
Explicit content: | No |
Aspect Ratio: | 16:9 |
Screencast: | No |
Bumper: | UCS Default |
Trailer: | UCS Default |
Abstract: | The theory of structured deformations in the SBV setting developed by Chocki & Fonseca [1]
only takes into account the linear dependance on jumps along the approximating sequences. Following a model from Del Piero & Owen [2] that captures the non-linear dependence on jumps, the present approach to relaxation of non-local energies rests on two limiting processes: start from a submacroscopical level where we have a weighted average of disarrangements within neighborhoods of fixed size r > 0 and pass to the macrolevel, permitting disarrangements to diffuse through such a neighborhood. This limiting process determines a structured deformation as well as the non-local dependence of the energy density of such a structured deformation. Pass to the limit as r ! 0, to obtain purely local bulk and interfacial energy densities for the structured deformation identified in the first step. This is a joint work with Marco Morandotti, Dipartimento di Scienze Matematiche “G. L. Lagrange”, Politecnico di Torino, David R. Owen, Department of Mathematical Sciences, Carnegie Mellon University, Elvira Zappale, Dipartimento di Ingegneria Industriale, Università degli Studi di Salerno. References [1] R. Choksi and I. Fonseca: Bulk and interfacial energy densities for structured deformations of continua. Arch. Rational Mech. Anal. 138 (1997), 37-103. [2] G. Del Piero and D. R. Owen: Structured Deformations: Part Two. Quaderni |
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