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Archive of Applied Mechanics
Published in: Archive of Applied Mechanics 3/2019

05-06-2018 | Special

Universal spherically symmetric solution of nonlinear dislocation theory for incompressible isotropic elastic medium

Authors: Evgeniya V. Goloveshkina, Leonid M. Zubov

Published in: Archive of Applied Mechanics | Issue 3/2019

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Abstract

The equilibrium problem of a nonlinearly elastic medium with a given dislocation distribution is considered. The system of equations consists of the equilibrium equations for the stresses, the incompatibility equations for the distortion tensor, and the constitutive equations. Deformations are considered to be finite. For a special distribution of screw and edge dislocations, an exact spherically symmetric solution of these equations is found. This solution is universal in the class of isotropic incompressible elastic bodies. With the help of the obtained solution, the eigenstresses in a solid elastic sphere and in an infinite space with a spherical cavity are determined. The interaction of dislocations with an external hydrostatic load was also investigated. We have found the dislocation distribution that causes the spherically symmetric quasi-solid state of an elastic body, which is characterized by zero stresses and a nonuniform elementary volumes rotation field.
previous article Introduction to the Special Issue in honor of Konstantin Lurie
next article Dynamic equations for a periodic set of edge dislocations

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Metadata
Title
Universal spherically symmetric solution of nonlinear dislocation theory for incompressible isotropic elastic medium
Authors
Evgeniya V. Goloveshkina
Leonid M. Zubov
Publication date
05-06-2018
Publisher
Springer Berlin Heidelberg
Published in
Archive of Applied Mechanics / Issue 3/2019
Print ISSN: 0939-1533
Electronic ISSN: 1432-0681
DOI
https://doi.org/10.1007/s00419-018-1403-9

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