Abstract
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.
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Goloveshkina, E.V., Zubov, L.M. (2019). Eigenstresses in a Nonlinearly Elastic Sphere with Distributed Dislocations. In: Abali, B., Altenbach, H., dell'Isola, F., Eremeyev, V., Öchsner, A. (eds) New Achievements in Continuum Mechanics and Thermodynamics. Advanced Structured Materials, vol 108. Springer, Cham. https://doi.org/10.1007/978-3-030-13307-8_11
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DOI: https://doi.org/10.1007/978-3-030-13307-8_11
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