Arch Appl Mech https://doi.org/10.1007/s00419-018-1403-9 ORIGINAL Evgeniya V. Goloveshkina · Leonid M. Zubov Universal spherically symmetric solution of nonlinear dislocation theory for incompressible isotropic elastic medium Received: 24 November 2017 / Accepted: 26 May 2018 © Springer-Verlag GmbH Germany, part of Springer Nature 2018 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. Keywords Nonlinear elasticity · Dislocation density · Eigenstresses · Large deformations · Exact
Archive of Applied Mechanics – Springer Journals
Published: Jun 5, 2018
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