Abstract
In this paper, we consider the inverse problem of continuum mechanics, in which, given the kinematics of the flow of a homogeneous incompressible material in all three-dimensional space, it is required to determine the force modes that provide such kinematics according to the equations of motion and the chosen constitutive relations. The adopted law of motion of particles consists of three time stages, each of which corresponds to compression in one direction and spreading of the medium in two others. In this case, the planes parallel to the Cartesian coordinate planes before deformation remain parallel to them at any time of the process. This allows the problem of sequential triaxial compression of a parallelepiped and its transfer from the initial position to a specified final one to be posed. The possible kinematic and force modes for the implementation of this translation are found.
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Funding
This work was performed within the framework of the state assignment no. AAAA-A20-120011690136-2 and was supported by the Russian Foundation for Basic Research, grant nos. 18-29-10085mk and 19-01-00016a.
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To the 70th Anniversary of Evgenii Nikolaevich Chumachenko (1951–2015)
Translated by A. Ivanov
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Georgievskii, D.V. Sequential Triaxial Dynamic Compression of a Parallelepiped. Mech. Solids 56, 1651–1656 (2021). https://doi.org/10.3103/S0025654421080082
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DOI: https://doi.org/10.3103/S0025654421080082