Geodesic
Calculation of dynamic destruction in deformable bodies
Matematičeskoe modelirovanie, Tome 29 (2017) no. 4, pp. 45-58.

Voir la notice de l'article provenant de la source Math-Net.Ru

The aim of this work is to study the possibilities of application of grid-characteristic method on structural grids for problems of destruction in solid deformable bodies. Models of shear damage and cracking were used. Problems of collisions and the problem of seismic stability of surface facilities were discovered. Grid-characteristic method, developed for the problems of the dynamic behavior of deformable solids, is used for the numerical solution of these problems.
Keywords: mathematical modeling, cracks, hexahedral grids, grid-characteristic method, continuum mechanics, spall effect, seismic.
Mots-clés : destruction 
@article{MM_2017_29_4_a3,
     author = {D. P. Grigorievih and N. I. Khokhlov and I. B. Petrov},
     title = {Calculation of dynamic destruction in deformable bodies},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {45--58},
     publisher = {mathdoc},
     volume = {29},
     number = {4},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2017_29_4_a3/}
}
TY  - JOUR
AU  - D. P. Grigorievih
AU  - N. I. Khokhlov
AU  - I. B. Petrov
TI  - Calculation of dynamic destruction in deformable bodies
JO  - Matematičeskoe modelirovanie
PY  - 2017
SP  - 45
EP  - 58
VL  - 29
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2017_29_4_a3/
LA  - ru
ID  - MM_2017_29_4_a3
ER  - 
%0 Journal Article
%A D. P. Grigorievih
%A N. I. Khokhlov
%A I. B. Petrov
%T Calculation of dynamic destruction in deformable bodies
%J Matematičeskoe modelirovanie
%D 2017
%P 45-58
%V 29
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2017_29_4_a3/
%G ru
%F MM_2017_29_4_a3
D. P. Grigorievih; N. I. Khokhlov; I. B. Petrov. Calculation of dynamic destruction in deformable bodies. Matematičeskoe modelirovanie, Tome 29 (2017) no. 4, pp. 45-58. http://geodesic.mathdoc.fr/item/MM_2017_29_4_a3/

[1] Kholodov A. S., “Chislennye metody resheniya uravnenia i sistem giperbolicheskogo tipa”, Entsiklopedia nizkotemperaturnoy plazmy (seriya "B"), ch. 2, v. VII-1, Matematicheskoe modelirovanie v nizkotemperaturnoy plazme, Izdatelstvo «YaNUS-K», M., 2009, 141–174

[2] Machen J., Sak S., “Method for prediction «Tenzor»”, Methods in computational physics advanced in research and application, v. 3, Academic Press, NY, 1967, 185–211

[3] Kukudzhanov V. N., Vychislitelnaya mekhanika sploshnykh sred, Fizmatlit, M., 2008, 320 pp.

[4] Petrov I. B., Chelnokov F. B., “Numerical analysis of wave processes and fracture in layered targets”, Computational Mathematics and Mathematical Physics, 43:10 (2003), 1503–1519 | MR | Zbl

[5] Petrov I. B., Holodov A. S., “Numerical study of some dynamic problems of the mechanics of a deformable rigid body by the mesh-characteristic method”, USSR Computational Mathematics and Mathematical Physics, 24:3 (1984), 61–73 | DOI | MR | Zbl | Zbl

[6] Petrov I. B., Tormasov A. G., “Chislennoe issledovanie kosogo soudareniia zhestkogo sharika s dvukhsloinoi uprugoplasticheskoi plitoi”, Matem. modelirovanie, 4:3 (1992), 20–27

[7] Harten A., Osher S., “Uniformly high-order accurate nonoscillatory schemes”, SIAM J. Numer. Anal., 24:2 (1987), 279–309 | DOI | MR | Zbl

[8] Ivanov V. D., Kondaurov V. I., Petrov I. B., Kholodov A. S., “Raschet dinamicheskogo deformirovaniia i razrusheniia uprugoplasticheskikh tel setochno-kharakteristicheskimi metodami”, Matem. modelirovanie, 2:11 (1990), 10–29 | Zbl

[9] Kondaurov V. I., “Continual fracturing of nonlinearly elastic bodies”, J. Appl. Math. Mech., 52:2 (1989), 237–243 | DOI | MR | Zbl

[10] Kholodov A. S., Kholodov Ya. A., “Monotonicity criteria for difference schemes designed for hyperbolic equations”, Computational Mathematics and Mathematical Physics, 46:9 (2006), 1560–1588 | DOI | MR

[11] Burago N. G., Kukudzhanov V. N., “A review of contact algorithms”, A Journal of Russian Academy of Sciences, Mechanics of Solids, 40:1 (2005), 35–71

[12] Qianyi Chen, Jingtao Wang, Kaixin Liu, “Improved CE/SE scheme with particle level set method for numerical simulation of spall fracture due to high-velocity impact”, Journal of Computational Physics, 229 (2010), 7503–7519 | DOI | Zbl

[13] Gagnon R. E., Wang J., “Numerical simulations of a tanker collision with a bergy bit incorporating hydrodynamics, a validated ice model and damage to the vessel”, Cold Regions Science and Technology, 81 (2012), 26–35 | DOI

[14] Shuang Zhanga, Chun-an Tangb, Xiang-dong Zhangc, Zhe-cheng Zhangc, Jia-xu Jinc, “Cumulative plastic strain of frozen aeolian soil under highway dynamic loading”, Cold Regions Science and Technology, 120 (2015), 89–95 | DOI