Persona: Jiménez Morales, Víctor Manuel
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Jiménez Morales
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Víctor Manuel
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Publicación On the Homogeneity of Non-uniform Material Bodies(Springer, 2020) León, Manuel de; Epstein, Marcelo; Jiménez Morales, Víctor ManuelA 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.Publicación The evolution equation: an application of groupoids to material evolution(CSIC, 2021) León, Manuel de; Jiménez Morales, Víctor ManuelThe aim of this paper is to study the evolution of a material point of a body by itself, and not the body as a whole. To do this, we construct a groupoid encoding all the intrinsic properties of the material point and its characteristic foliations, which permits us to define the evolution equation. We also discuss phenomena like remodeling and aging.Publicación New notions of uniformity and homogeneity of Cosserat media(AIP Publising, 2023) León, Manuel de; Jiménez Morales, Víctor ManuelIn this paper, we study internal properties of Cosserat media. In fact, by using groupoids and smooth distributions, we obtain three canonical equations. The non-holonomic material equation for Cosserat media characterizes the uniformity of the material. The holonomic material equation for Cosserat media permits us to study when a Cosserat material is a second-grade material. It is remarkable that these two equations also provide us a unique and maximal division of the Cosserat medium into uniform and second-grade parts, respectively. Finally, we present a proper definition of homogeneity of the Cosserat medium, which does not need to assume uniformity. Thus, the homogeneity equation for Cosserat media characterizes this notion of homogeneity.Publicación A geometric model for non-uniform processes of morphogenesis(Elsevier, 2022-09-23) León, Manuel de; Jiménez Morales, Víctor ManuelIn this paper we present an application of the groupoid theory to the study of relevant case of material evolution phenomena, the process of morphogenesis. Our theory is inspired by Walter Noll’s theories of continuous distributions and provides a unifying and very simple framework of these phenomena. We present the explicit equation, the morphogenesis equation, to calculate the material distributions associated to this phenomenon.Publicación Material Geometry: Groupoids in Continuum Mechanics(World Scientific Publishing Co. Pte. Ltd., 2021) León, Manuel de; Epstein, Marcelo; Jiménez Morales, Víctor ManuelThis 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.Publicación Characteristic foliations of material evolution: from remodeling to aging(SAGE Publications, 2022) León, Manuel de; Epstein, Marcelo; Jiménez Morales, Víctor ManuelFor 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.Publicación Contact Hamiltonian and Lagrangian systems with nonholonomic constraints(American Institute of Mathematical Sciences, 2021) León, Manuel de; Lainz Valcázar, Manuel; Jiménez Morales, Víctor ManuelIn this article we develop a theory of contact systems with nonholonomic constraints. We obtain the dynamics from Herglotz's variational principle, by restricting the variations so that they satisfy the nonholonomic constraints. We prove that the nonholonomic dynamics can be obtained as a projection of the unconstrained Hamiltonian vector field. Finally, we construct the nonholonomic bracket, which is an almost Jacobi bracket on the space of observables and provides the nonholonomic dynamics.