Coupled Dynamic Thermoplasticity Problem for Transversely Isotropic Parallelepiped

The article frmulates a coupled thermoplastic dynamic boundary value problem based on the deformation theory of transversally isotropic bodies. The coupled boundary value problem consists of the motion equation, the thermoplasticity constitutive relations for transversely isotropic bodies, the Cauchy relation and the heat conduction equation, with the corresponding initial and boundary conditions. A coupled dynamic boundary value problem for a thermoplastic transversely isotropic parallelepiped is considered. For the numerical solution of the coupled boundary value problem, an explicit finite-difference schemes are constructed. The finite-difference equations are written in the form of recurrent relations allowing to find the components of displacement and temperature, taking into account the initial and boundary conditions at each layer in time. On the basis of the obtained numerical results, the stress-strain state of a transversely isotropic thermoplastic parallelepiped is investigated and the propagation of the plastic zone is shown.

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