Sequential Triaxial Dynamic Compression of a Parallelepiped
The inverse problem of continuum mechanics is considered, in which the given kinematics of the flow of a homogeneous incompressible material in the three-dimensional space requires determining the force modes that provide such kinematics according to the equations of motion and the selected constitutive relations. The accepted law of particle motion consists of three time stages, each of which corresponds to compression in one direction and spreading of the medium in the other two. In this case, the planes that were parallel to the Cartesian coordinate planes before the deformation remain parallel to them at any time of the process. This makes it possible to formulate the problem of sequential triaxial compression of a parallelepiped and its translation from the initial position to the specified final one. The possible kinematic and force modes for implementing this translation are obtained.