Geodesic
Dynamics of plane strains in heteromodular isotropic elastic media
Sibirskij žurnal industrialʹnoj matematiki, Tome 24 (2021) no. 1, pp. 18-31

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Under consideration are the features of nonlinear dynamics of a heteromodular elastic medium under the plane strain. A mathematical model of the heteromodular isotropic elastic medium is given by a stress-strain relation with variable elastic moduli that are nonanalytic functions of deformation invariants. In this case, we show that the two plane-polarized combined shock waves called quasi-longitudinal and quasi-transverse ones can appear in the material. To calculate the velocities of these waves, we obtain some formulas that include the parameters of both the prior deformed state and the boundary impact action. By example, we solve the two-dimensional self-similar boundary value problem concerning the reflection of a plane shock compression wave from a rigid obstacle and demonstrate how to use the information on the types of nonlinear waves in the heteromodular medium. We show that the nature of the wave fronts in the reflected wavepackage depends significantly on the incident angle of the shock compression wave.
Keywords: heteromodular elasticity, dynamic deformation, plane strain, shock wave, the Riemann wave, self-similar problem, numerical experiment. 
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     author = {O. V. Dudko and A. A. Mantsybora},
     title = {Dynamics of plane strains in heteromodular isotropic elastic media},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {18--31},
     publisher = {mathdoc},
     volume = {24},
     number = {1},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2021_24_1_a1/}
}
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O. V. Dudko; A. A. Mantsybora. Dynamics of plane strains in heteromodular isotropic elastic media. Sibirskij žurnal industrialʹnoj matematiki, Tome 24 (2021) no. 1, pp. 18-31. http://geodesic.mathdoc.fr/item/SJIM_2021_24_1_a1/