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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2017 - 201952020 - 20221
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Autor: Epstein, Marcelo × Tiene archivos: true ×

Resultados de la búsqueda

Mostrando 1 - 6 de 6
  • Miniatura
    Publicación
    Lie groupoids and algebroids applied to the study of uniformity and homogeneity of material bodies
    (American Institute of Mathematical Sciences, 2018) León, Manuel de; Epstein, Marcelo; Jiménez Morales, Víctor Manuel
    A Lie groupoid, called material Lie groupoid, is associated in a natural way to any elastic material. The corresponding Lie algebroid, called material algebroid, is used to characterize the uniformity and the homogeneity properties of the material. The relation to previous results in terms of G−structures is discussed in detail. An illustrative example is presented as an application of the theory.
  • Miniatura
    Publicación
    Material geometry
    (Springer, 2019) Epstein, Marcelo; León, Manuel de; Jiménez Morales, Víctor Manuel
    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.
  • Miniatura
    Publicación
    Lie groupoids and algebroids applied to the study of uniformity and homogeneity of Cosserat media
    (World Scientific, 2018) León, Manuel de; Epstein, Marcelo; Jiménez Morales, Víctor Manuel
    A Lie groupoid, called second-order non-holonomic material Lie groupoid, is associated in a natural way to any Cosserat medium. This groupoid is used to give a new definition of homogeneity which does not depend on a material archetype. The corresponding Lie algebroid, called second-order non-holonomic material Lie algebroid, is used to characterize the homogeneity property of the material. We also relate these results with the previously obtained ones in terms of non-holonomic second-order G¯¯¯¯ -structures.
  • Miniatura
    Publicación
    Material distributions
    (SAGE, 2017) León, Manuel de; Epstein, Marcelo; Jiménez Morales, Víctor Manuel
    The concept of material distribution is introduced as describing the geometric material structure of a general nonuniform body. Any smooth constitutive law is shown to give rise to a unique smooth integrable singular distribution. Ultimately, the material distribution and its associated singular foliation result in a rigorous and unique subdivision of the material body into strictly smoothly uniform components. Thus, the constitutive law induces a unique partition of the body into smoothly uniform sub-bodies, laminates, filaments and isolated points.
  • Miniatura
    Publicación
    Characteristic foliations of material evolution: from remodeling to aging
    (SAGE Publications, 2022) León, Manuel de; Epstein, Marcelo; Jiménez Morales, Víctor Manuel
    For any body-time manifold (Formula presented.) there exists a groupoid, called the material groupoid, encoding all the material properties of the material evolution. A smooth distribution, the material distribution, is constructed to deal with the case in which the material groupoid is not a Lie groupoid. This new tool provides a unified framework to deal with general non-uniform material evolution.
  • Miniatura
    Publicación
    Characteristic distribution: An application to material bodies
    (Elsevier, 2018) León, Manuel de; Epstein, Marcelo; Jiménez Morales, Víctor Manuel
    Associated to each material body B there exists a groupoid (B) consisting of all the material isomorphisms connecting the points of B. The uniformity character of B is reflected in the properties of (B): B is uniform if, and only if, (B) is transitive. Smooth uniformity corresponds to a Lie groupoid and, specifically, to a Lie subgroupoid of the groupoid 1 (B,B) of 1- jets of B. We consider a general situation when (B) is only an algebraic subgroupoid. Even in this case, we can cover B by a material foliation whose leaves are transitive. The same happens with (B) and the corresponding leaves generate transitive Lie groupoids (roughly speaking, the leaves covering B). This result opens the possibility to study the homogeneity of general material bodies using geometric instruments.