Geodesic
On the impact deformation of an incompressible half-space under the action of a~shear load of variable direction
Sibirskij žurnal industrialʹnoj matematiki, Tome 17 (2014) no. 2, pp. 87-96

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A loading process in which the shear action on the boundary plane changes both in intensity and direction is considered on the example of a one-dimensional plane problem for a nonlinear elastic incompressible half-space. We show that, in the domains of the space where the nonlinearity of the system becomes a substantial factor, in the front region of the shock wave, the solution is determined by a system of nonlinear evolution equations. We obtain the general solution to the evolution system. As an example, we consider a particular solution to the evolution system for one of the simplest boundary conditions. We also expose a parametric method for finding the displacements on the basis of a solution to the evolution system.
Keywords: nonlinear elastic incompressible medium, transverse shock wave, shear load of variable direction, evolution equations for the change of shear intensity and shear direction. 
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     author = {V. E. Ragozina and Yu. E. Ivanova},
     title = {On the impact deformation of an incompressible half-space under the action of a~shear load of variable direction},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {87--96},
     publisher = {mathdoc},
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     number = {2},
     year = {2014},
     language = {ru},
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V. E. Ragozina; Yu. E. Ivanova. On the impact deformation of an incompressible half-space under the action of a~shear load of variable direction. Sibirskij žurnal industrialʹnoj matematiki, Tome 17 (2014) no. 2, pp. 87-96. http://geodesic.mathdoc.fr/item/SJIM_2014_17_2_a8/