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Journal of Elasticity

, Volume 135, Issue 1–2, pp 237–260 | Cite as

Material Geometry

  • Marcelo EpsteinEmail author
  • Víctor Manuel Jiménez
  • Manuel de León
Article

Abstract

Walter Noll’s trailblazing constitutive theory of material defects in smoothly uniform bodies is recast in the language of Lie groupoids and their associated Lie algebroids. From this vantage point the theory is extended to non-uniform bodies by introducing the notion of singular material distributions and the physically cognate idea of graded uniformity and homogeneity.

Keywords

Uniformity Homogeneity Groupoids Lie algebroids Singular distributions Stefan-Sussman theorem 

Mathematics Subject Classification

74A20 22A22 

Notes

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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.University of CalgaryCalgaryCanada
  2. 2.Instituto de Ciencias Matemáticas (CSIC-UAM-UC3M-UCM)MadridSpain

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