Material Geometry

Groupoids In Continuum Mechanics

By: Manuel De Leon, Marcelo Epstein, Victor Manuel Jimenez

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Hardcover | 9 May 2021

At a Glance

Hardcover
226 Pages

Dimensions(cm)
22.86 x 15.24 x 1.42

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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.

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