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Unified geometric
formulation of material uniformity and evolution
Marcelo Epstein and Manuel de León
Vol. 4 (2016), No. 1, 17–29
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Abstract |
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The differential-geometric underpinnings of a unified theory of material uniformity and evolution are exposed in terms of the language of groupoids subordinate to geometric distributions. Both the standard theory of material uniformity and the extended theory of functionally graded materials are included in the formulation as well as their temporal counterparts in anelastic and aging processes. |
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Dedicated to Gérard Maugin, in gratitude for many years of inspiration and friendship |
Keywords
groupoids, distributions, material uniformity, material
evolution, body-time manifold, groupoid actions, aging,
morphogenesis
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Mathematical Subject Classification 2010
Primary: 74A20
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Milestones
Received: 25 July 2015
Revised: 9 December 2015
Accepted: 6 February 2016
Published: 29 February 2016
Communicated by Raffaele Esposito
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Authors |
| Marcelo Epstein | |
| Department of Mechanical and
Manufacturing Engineering University of Calgary 2500 University Drive NW Calgary, AB T2N 1N4 Canada |
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| Manuel de León | |
| Instituto de Ciencias
Matemáticas CSIC-UAM-UC3M-UCM Nicolás Cabrera, 13-15 28049 Madrid Spain |
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