Mathematical and Numerical Modeling of the Coupled Dynamic Thermoplastic Problem

Using the strain space and deformation thermoplasticity theories the coupled dynamic thermoplastic boundary value problems are formulated. Strain space thermoplasticity theory, in contrast to the deformation one, allows formulating the coupled thermoplastic boundary value problems for the displacement and temperature increments. As an example, in one-dimensional case, the explicit and implicit types of finite difference equations are constructed. The numerical solution of the explicit finite difference equations reduced to the application of the recurrent formulas, whereas the implicit scheme reduced to the application of the elimination method. Comparison shows that the numerical results obtained using explicit and implicit scheme coincides.

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