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Published in:
2019 | OriginalPaper | Chapter
Eigenstresses in a Nonlinearly Elastic Sphere with Distributed Dislocations
Authors : Evgeniya V. Goloveshkina, Leonid M. Zubov
Published in: New Achievements in Continuum Mechanics and Thermodynamics
Publisher: Springer International Publishing
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The problem of the eigenstresses due to distributed edge and screw dislocations in a hollow nonlinearly elastic sphere is considered. The dislocation density is given by an arbitrary spherically symmetric tensor field. For a general isotropic elastic material, the problem is reduced to a one-dimensional nonlinear boundary value problem. By replacing the unknown functions, the boundary value problem with nonlinear boundary conditions is transformed to a problem with linear ones. Numerical solutions are constructed for specific models of compressible and incompressible materials. The analysis of the influence of dislocations on a stress state of an elastic sphere at large deformations is carried out.