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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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