caa a22 4500 605515042 CHVBK 20210128100707.0 cr unu---uuuuu 210128e20150601xx s 000 0 eng 10.1007/s00205-014-0825-y doi (NATIONALLICENCE)springer-10.1007/s00205-014-0825-y Metric Description of Singular Defects in Isotropic Materials [Elektronische Daten] [Raz Kupferman, Michael Moshe, Jake Solomon] Classical elasticity is concerned with bodies that can be modeled as smooth manifolds endowed with a reference metric that represents local equilibrium distances between neighboring material elements. The elastic energy associated with the configuration of a body in classical elasticity is the sum of local contributions that arise from a discrepancy between the actual metric and the reference metric. In contrast, the modeling of defects in solids has traditionally involved extra structure on the material manifold, notably torsion to quantify the density of dislocations and non-metricity to represent the density of point defects. We show that all the classical defects can be described within the framework of classical elasticity using tensor fields that only assume a metric structure. Specifically, bodies with singular defects can be viewed as affine manifolds; both disclinations and dislocations are captured by the monodromy that maps curves that surround the loci of the defects into affine transformations. Finally, we showthat two dimensional defectswith trivial monodromy are purely local in the sense that if we remove from the manifold a compact set that contains the locus of the defect, the punctured manifold can be isometrically embedded in a Euclidean space. Springer-Verlag Berlin Heidelberg, 2014 Kupferman Raz Institute of Mathematics, The Hebrew University, 91904, Jerusalem, Israel aut Moshe Michael Racah Institute of Physics, The Hebrew University, 91904, Jerusalem, Israel aut Solomon Jake Institute of Mathematics, The Hebrew University, 91904, Jerusalem, Israel aut Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 216/3(2015-06-01), 1009-1047 0003-9527 216:3<1009 2015 216 205 https://doi.org/10.1007/s00205-014-0825-y text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00205-014-0825-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Kupferman Raz Institute of Mathematics, The Hebrew University, 91904, Jerusalem, Israel aut NATIONALLICENCE 700 1- Moshe Michael Racah Institute of Physics, The Hebrew University, 91904, Jerusalem, Israel aut NATIONALLICENCE 700 1- Solomon Jake Institute of Mathematics, The Hebrew University, 91904, Jerusalem, Israel aut NATIONALLICENCE 773 0- Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 216/3(2015-06-01), 1009-1047 0003-9527 216:3<1009 2015 216 205