Material Geometry of Binary Composites

  title={Material Geometry of Binary Composites},
  author={Marcelo Epstein},
The constitutive characterization of the uniformity and homogeneity of binary elastic composites is presented in terms of a combination of the material groupoids of the individual constituents. The incorporation of these two groupoids within a single double groupoid is proposed as a viable mathematical framework for a unified formulation of this and similar kinds of problems in continuum mechanics. 
Double groupoids in the theory of material uniformity
The use of double groupoids and their associated double Lie algebroids and characteristic distributions is proposed for the description and analysis of continuous media that carry two different


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Determination of a double Lie groupoid by its core diagram
Nonlinear elastic inclusions in isotropic solids
  • A. Yavari, A. Goriely
  • Mathematics
    Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
  • 2013
A geometric framework to calculate the residual stress fields and deformations of nonlinear solids with inclusions and eigenstrains is introduced and it is shown how singularities in the stress distribution emerge as a consequence of a mismatch between radial and circumferential eigen Strains at the centre of a sphere or the axis of a cylinder.
Material distributions
The concept of material distribution is introduced as describing the geometric material structure of a general non-uniform body. Any smooth constitutive law is shown to give rise to a unique smooth
Material Geometry, Doctoral Thesis, UAM-ICMAT, Spain, Victor Jimenez.pdf
  • 2019
Material groupoids and algebroids, Mathematics and Mechanics of Solids
  • 2019
Material Geometry
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Lie groupoids and their associated algebroids arise naturally in the study of the constitutive properties of continuous media. Thus, continuum mechanics and differential geometry illuminate each
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