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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
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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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