Mathematical modelling of mechanics problems
Ragozina V., Ivanova Yu.
The evolution equation of the one-dimensional axisymmetric problem of the propagation of deformations
Abstract: In the article, consideration is being given to the solution to the one-dimensional axial symmetry problem dealing with the transverse motion of a shock wave. The shock wave that propagates from the cylindrical cavity in a nonlinear elastic incompressible space is a result of a torsional load at the border. The application of the method of matched asymptotic expansions leads to the evolution equation in the frontal region of the shock wave. The obtained equation differs fundamentally from the evolution equations describing the propagation of plane longitudinal and transverse shock waves.
Key words: nonlinear elasticity, compressibility, shock wave, evolution equation, perturbation method.
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