Construction of Nonsingular Stress Fields for Non-Euclidean Model in Planar Deformations
-
Published:2021-12
Issue:6
Volume:14
Page:815-821
-
ISSN:1997-1397
-
Container-title:Journal of Siberian Federal University. Mathematics & Physics
-
language:
-
Short-container-title:J. Sib. Fed. Univ., Math. phys.
Author:
Guzev Mikhail A., ,Riabokon Evgenii P.
Abstract
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
Publisher
Siberian Federal University
Subject
General Physics and Astronomy,General Mathematics