Geodesic
Mathematical simulation of deformation and wave processes in multilayered structures
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 9, pp. 1690-1696

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The deformation and wave processes induced by collisions of an impactor with deformable layered targets of various configurations are analyzed. The numerical solution of such problems is associated with an adequate treatment of wave processes in a continuous medium, which is an especially difficult task in the case of layered targets. To deal with the former problem, it is proposed to use adaptive Lagrangian triangular meshes. Wave processes are simulated using the grid-characteristic method, which can serve as a basis for algorithms that do not fail near the boundary of the computational domain and at numerous material interfaces. Additionally, hybrid and hybridized grid-characteristic schemes are applied that substantially improve numerical solutions with steep gradients (discontinuous solutions). These methods provide an adequate treatment of wave processes in layered targets (wave reflection and refraction at contact surfaces, secondary-wave interaction, changes in the conditions on these boundaries, etc.). 
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     author = {N. G. Matyushev and I. B. Petrov},
     title = {Mathematical simulation of deformation and wave processes in multilayered structures},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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     publisher = {mathdoc},
     volume = {49},
     number = {9},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_9_a14/}
}
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N. G. Matyushev; I. B. Petrov. Mathematical simulation of deformation and wave processes in multilayered structures. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 9, pp. 1690-1696. http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_9_a14/