Material Geometry: Groupoids In Continuum Mechanics
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A01=Manuel De Leon
A01=Marcelo Epstein
A01=Victor Manuel Jimenez
Algebroids
Author_Manuel De Leon
Author_Marcelo Epstein
Author_Victor Manuel Jimenez
Category=PHDD
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G-structures
Groupoids
Homogeneity
Integrability
Uniformity
Product details
- ISBN 9789811232541
- Publication Date: 10 May 2021
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
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This monograph is the first in which the theory of groupoids and algebroids is applied to the study of the properties of uniformity and homogeneity of continuous media. It is a further step in the application of differential geometry to the mechanics of continua, initiated years ago with the introduction of the theory of G-structures, in which the group G denotes the group of material symmetries, to study smoothly uniform materials.The new approach presented in this book goes much further by being much more general. It is not a generalization per se, but rather a natural way of considering the algebraic-geometric structure induced by the so-called material isomorphisms. This approach has allowed us to encompass non-uniform materials and discover new properties of uniformity and homogeneity that certain material bodies can possess, thus opening a new area in the discipline.
