Vol. 4, No. 1, 2016

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ISSN: 2325-3444 (e-only)
ISSN: 2326-7186 (print)
Unified geometric formulation of material uniformity and evolution

Marcelo Epstein and Manuel de León

Vol. 4 (2016), No. 1, 17–29
Abstract

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.

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
Mathematical Subject Classification 2010
Primary: 74A20
Milestones
Received: 25 July 2015
Revised: 9 December 2015
Accepted: 6 February 2016
Published: 29 February 2016

Communicated by Raffaele Esposito
Authors
Marcelo Epstein
Department of Mechanical and Manufacturing Engineering
University of Calgary
2500 University Drive NW
Calgary, AB T2N 1N4
Canada
Manuel de León
Instituto de Ciencias Matemáticas
CSIC-UAM-UC3M-UCM
Nicolás Cabrera, 13-15
28049 Madrid
Spain