Persona:
Jiménez Morales, Víctor Manuel

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0000-0003-3135-3303
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Jiménez Morales
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Víctor Manuel
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2020 - 20212
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Tipo de ítem: Publication × Tipo: book ×

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  • No hay miniatura disponible
    Publicación
    On the Homogeneity of Non-uniform Material Bodies
    (Springer, 2020) León, Manuel de; Epstein, Marcelo; Jiménez Morales, Víctor Manuel
    A groupoid (B) called material groupoid is naturally associated to any simple body B (see [11, 9, 10]). The material distribution is introduced due to the (possible) lack of differentiability of the material groupoid (see [13, 15]). Thus, the inclusion of these new objects in the theory of material bodies opens the possibility of studying non-uniform bodies. As an example, the material distribution and its associated singular foliation result in a rigorous and unique subdivision of the material body into strictly smoothly uniform sub-bodies, laminates, filaments and isolated points. Furthermore, the material distribution permits us to present a “measure" of uniformity of a simple body as well as more general definitions of homogeneity for non-uniform bodies.
  • No hay miniatura disponible
    Publicación
    Material Geometry: Groupoids in Continuum Mechanics
    (World Scientific Publishing Co. Pte. Ltd., 2021) León, Manuel de; Epstein, Marcelo; Jiménez Morales, Víctor Manuel
    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.