Geodesic
Construction of nonsingular stress fields for non-Euclidean model in planar deformations
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 14 (2021) no. 6, pp. 815-821

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A material with a microstructure is considered. A material is described on the basis of a non-Euclidean model of a continuous medium. In equilibrium, the total stress field is represented as the sum of elastic and self-balanced stresses, the parameterization of which is given through the scalar curvature of the Ricci tensor. It is proposed to use the spectral biharmonic equation to calculate the scalar curvature. Using the example of a plane strain state of a material, it is shown that the amplitude coefficients of elastic and self-balanced fields can be chosen so that singularities of the same type compensate each other in the full stress field.
Keywords: nonsingular stress field, planar deformation, spectral biharmonic equation.
Mots-clés : microstructure 
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     title = {Construction of nonsingular stress fields for {non-Euclidean} model in planar deformations},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
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     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JSFU_2021_14_6_a14/}
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Мikhail A. Guzev; Evgenii P. Riabokon. Construction of nonsingular stress fields for non-Euclidean model in planar deformations. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 14 (2021) no. 6, pp. 815-821. http://geodesic.mathdoc.fr/item/JSFU_2021_14_6_a14/