МОДЕЛИРОВАНИЕ ПРОНИКАНИЯ НЕОСЕСИММЕТРИЧНЫХ ТЕЛ В ГРУНТ ПО ИНЕРЦИИ ПРИ УЧЕТЕ ТРЕНИЯ
Ключевые слова:
проникание, поверхностное трение, упругопластическая среда, конический ударник, пирамидальные тела, модель локального взаимодействия, трехмерное моделирование
Аннотация
Рассматривается задача о нормальном ударе и проникании жестких пространственных тел конечной массы в полупространство, занимаемое упруго-пластической грунтовой средой. Для среды проникания принимается модель линейно сжимаемой упругопластической среды Григоряна при линейной зависимости предела текучести от давления. Решение задачи осуществляется численно в трехмерной постановке с применением пакета программ LS-DYNA. Упругопластическая среда проникания рассматривается на неподвижной эйлеровой сетке с выделением пустых ячеек, в которые материал перетекает в процессе деформирования. Пространственные ударники моделируются жестким недеформируемым телом в лагранжевой системе координат.
Проводится исследование влияния поверхностного трения при проникании в упругопластическую грунтовую среду Григоряна ударников различной формы: круговой конус, четырехлучевая звезда и пирамидальное тело. По-перечное сечение звездообразного тела образовано двумя ромбами с отношением диагоналей 1:2, в основании пирамиды находится ромб с отношением диагоналей 1:3. Исследуемые тела имеют равные площади оснований и одинаковый наклон боковой поверхности (угол отсчитывается между направлением вектора скорости движения тела и нормалью к боковой поверхности). Для сравнения рассматривается также круговой конус основанием той же площади.
Движение ударников рассматривалось с постоянными скоростями и по инерции в диапазоне скоростей от 150 до 600 м/с, что соответствует дозвуковым и сверхзвуковым скоростям. Значение коэффициента поверхностного трения задавалось близким к значению коэффициента трения в сухом песчаном грунте естественного состава. Проведено сравнение с полученными ранее результатами расчетов при нулевом коэффициенте трения. Установлено, что сила сопротивления внедрению и глубина проникания может быть описана с применением двучленного квадратичного по скорости закона проникания Резаля. Отличия сил сопротивления внедрению пирамидального, конического и звездообразного тел одинаковой высоты находятся в пределах 10-20%.
Литература
1. Borg J.P., Morrissey M.P., Perich C.A., Vogler T.J., Chhabildas L.C. In situ velocity and stress characterization of a projectile penetrating a sand target: Experimental measurements and continuum simulations. Int. J. Impact Eng. 2013. Vol. 51. P. 23-35. http://dx.doi.org/10.1016/j.ijimpeng.2012.07.009.
2. Park H., Chen W. Stress variations and particle movements during penetration into granular materials. T. Proulx (ed.). Dynamic Behavior of Materials, Conference Proceedings of the Society for Experimental Mechanics Series 99. 2011. Vol. 1. P. 85-92. https://doi.org/10.1007/978-1-4614-0216-9_11.
3. Collins A.L., Addiss J.W., Walley S.M., Promratana K., Bobaru F., Proud W.G., William-son D.M. The effect of rod nose shape on the internal flow fields during the ballistic penetration of sand. Int. J. Impact Eng. 2011. Vol. 38. Iss. 12. P. 951-963. https://doi.org/10.1016/j.ijimpeng.2011.08.002.
4. Savvateev A.F., Budin A.V., Kolikov V.A., Rutberg P.G. High-speed penetration into sand. Int. J. Impact Eng. 2001. Vol. 26. Iss. 1-10. P. 675-681. https://doi.org/10.1016/S0734-743X(01)00132-4.
5. Allen W.A., Mayfield E.B., Morrison H.L. Dynamics of a projectile penetrating sand. J. Appl. Phys. 1957. Vol. 28. No 3. P. 370-376.
6. Allen W.A., Mayfield E.B., Morrison H.L. Dynamics of a projectile penetrating sand. Part II. J. Appl. Phys. 1957. Vol. 28. Iss. 3. P. 1331-1335. https://doi.org/10.1063/1.1722750.
7. Veldanov V.A., Markov V.A., Pusev V.I., Ruchko A.M., Sotskii M.Yu., Fedorov S.V. Computation of non-deformable striker penetration into low strength obstacles using piezoelectric accelerometry data. Technical Physics. 2011. Vol. 56. No 7. P. 992-1002. https://doi.org/10.1134/S1063784211070231 .
8. Balandin Vl.V., Balandin Vl.Vl., Bragov A.M., Kotov V.L. Experimental study of the dynamics of penetration of a solid body into a soil medium. Technical Physics. 2016. Vol. 61. No 6. P. 860-868. https://doi.org/10.1134/S1063784216060037 .
9. Bivin Yu.K., Simonov I.V. Mechanics of dynamic penetration into soil medium. Mechanics of Solids. 2010. Vol. 45. Iss. 6. P. 892-920. https://doi.org/10.3103/S0025654410060130.
10. Forrestal M.J., Norwood F.R., Longcope D.B. Penetration into targets described by locked hydrostats and shear strength. Int. J. Solids Struct. 1981. Vol. 17. Iss. 9. P. 915-924. https://doi.org/10.1016/0020-7683(81)90106-2.
11. Omidvar M., Malioche J.D., Bless S., Iskander M. Phenomenology of rapid projectile penetra-tion into granular soils. Int. J. Impact Eng. 2015. Vol. 85. P. 146-160. https://doi.org/10.1016/j.ijimpeng.2015.06.002.
12. Ben-Dor G., Dubinsky A., Elperin T. Engineering models of high speed penetration into geological shields. Cent. Eur. J. Eng. 2014. Vol. 4. Iss. 1. P. 1-19. https://doi.org/10.2478/s13531-013-0135-4.
13. Kotov V.L., Balandin V.V., Bragov A.M., Linnik E.Yu., Balandin V.V. Using a local-interaction model to determine the resistance to penetration of projectiles into sandy soil. J. Appl. Mech. Tech. Phys. 2013. Vol. 54. Iss. 4. P. 612-621. https://doi.org/10.1134/S0021894413040123.
14. Cuncheng Shi, Mingyang Wang, Jie Li, Mengshen Li. A model of depth calculation for projectile penetration into dry sand and comparison with experiments. Int. J. Impact Eng. 2014. Vol. 73. P. 112-122. https://doi.org/10.1016/j.ijimpeng.2014.06.010.
15. Linnik E.Yu., Kotov V.L., Konstantinov A.Yu. Modelirovanie protsessov dinamicheskogo vnedreniya prostranstvennykh tel v szhimaemuyu uprugoplasticheskuyu sredu [Modeling the processes of dynamic penetration of dimensional bodies in a compressible elastoplastic medium]. Vestnik PNIPU. Mekhanika [PNRPU Mechanics Bulletin]. 2017. No 4. P. 92-108. DOI: 10.15593/perm.mech/2017.4.07 (In Russian).
16. Bazhenov V.G., Kotov V.L. Chislenno-analiticheskiy metod issledovaniya ustoychivosti dvizheniya tel vrashcheniya v myagkikh gruntovykh sredakh [Numerical-analytical method for investigation the stability of motion of bodies of rotation in soft soil media]. Prikladnaya matematika i mekhanika [J. Appl. Math. Mech.]. 2017. Vol. 81. No. 6. P. 688-698 (In Russian).
17. Aptukov V.N., Khasanov A.R. Optimizatsiya parametrov sloistykh plit pri dinamicheskom pronikanii zhestkogo indentora s uchetom treniya i oslablyayushchego effekta svobodnykh poverkh-nostey [Optimization of parameters of layered plates during dynamic hard indenter penetration with friction and weakining effect of free surfaces]. Vestnik PNIPU. Mekhanika [PNRPU Mechanics Bulletin]. 2014. No 2. P. 48-75. DOI: 10.15593/perm.mech/2014.2.03 (In Russian).
18. Ben-Dor G., Dubinsky A., Elperin T. Shape optimization of high-speed penetrators: a review. Cent. Eur. J. Eng. 2012. Vol. 2. No 4. P. 473-482. DOI: 10.2478/s13531-012-0022-4.
19. Bazhenov V.G., Balandin V.V., Grigoryan S.S., Kotov V.L. Analysis of models for calculating the motion of solids of revolution of minimum resistance in soil media. J. Appl. Math. Mech. 2014. Vol. 78. Iss. 1. P. 65-76. https://dx.doi.org/10.1016/j.jappmathmech.2014.05.008.
20. Kotov V.L., Linnik E.Yu. Study of motion of optimal bodies in the soil of grid method. 11th International Conference on Mesh Methods for Boundary-value Problems and Applications. 20–25 Oct. 2016. Kazan. 2016. P. 012058. DOI:10.1088/1757-899X/158/1/012058.
21. Bazhenov V.G., Kotov V.L., Krylov S.V., Balandin V.V., Bragov A.M., Tsvetkova E.V. Experimental-theoretical analysis of non-stationary interaction of deformable impactors with soil. J. Appl. Mech. Tech. Phys. 2001. Vol. 42. Iss. 6. P. 1083-1089. https://doi.org/10.1023/A:1012590517033.
22. Balandin V.V., Bragov A.M., Igumnov L.A., Konstantinov A.Yu., Kotov V.L., Lomunov A.K. Dynamic deformation of soft soil media: Experimental studies and mathematical modeling. Mecha-nics of Solids. 2015. Vol. 50. Iss. 3. P. 286-293. https://doi.org/10.3103/S002565441503005X.
23. Bazhenov V.G., Bragov A.M., Kotov V.L. Experimental-theoretical study of the penetration of rigid projectiles and identification of soil properties. J. Appl. Mech. Tech. Phys. 2009. Vol. 50. Iss. 6. P. 1011-1019. https://doi.org/10.1007/s10808-009-0135-6.
24. Bazhenov V.G., Bragov A.M., Kotov V.L., Kochetkov A.V. An investigation of the impact and penetration of solids of revolution into soft earth. J. Appl. Math. Mech. 2003. Vol. 67. Iss. 4. P. 611-620. https://doi.org/10.1016/S0021-8928(03)90064-5.
25. Grujicica M., Pandurangan B., Qiao R., Cheeseman B.A., Roy W.N., Skaggs R.R., Gupta R. Parameterization of the porous-material model for sand with different levels of water saturation. Soil Dynam. Earthquake Eng. 2008. Vol. 28. P. 20-35. https://doi.org/10.1016/j.soildyn.2007.05.001.
26. Bazhenov V.G., Kotov V.L., Kochetkov A.V., Krylov S.V., Feldgun V.R. Chislennoe modeli-rovanie nagruzheniya peschanogo grunta vzryvom nakladnogo zaryada [On wave processes in soil subjected to a surface charge explosion]. Izvestiya RAN. Mekhanika tverdogo tela [Mechanics of Solids]. 2001. Vol 36. Iss. 2. P. 62-68 (In Russian).
27. Borg J.P., Vogler T.J. Mesoscale simulations of a dart penetrating sand. Int. J. Impact Eng. 2008. Vol. 35. Iss. 12. P. 1435-1440. https://doi.org/10.1016/j.ijimpeng.2008.07.064.
28. Tran Q.A., Chevalier B., Breul P. Discrete modeling of penetration tests in constant velocity and impact conditions. Comput. Geotech. 2016. Vol. 71. P. 12-18. https://doi.org/10.1016/j.compgeo.2015.08.010.
29. Bo/rvik T., Dey S., Olovsson L. Penetration of granular materials by small-arms bullets. Int. J. Impact Eng. 2015. Vol. 75. P. 123-139. https://doi.org/10.1016/j.ijimpeng.2014.07.016.
30. Qin Fang, Jinhua Zhang, Yadong Zhang, Jinchun Liu. Mesoscopic investigation of the sand particulate system subjected to intense dynamic loadings. Int. J. Impact Eng. 2016. Vol. 89. P. 62-71. https://doi.org/10.1016/j.ijimpeng.2015.11.009.
31. Zhang L., Lambert S., Nicot F. Discrete dynamic modelling of the mechanical behaviour of a granular soil. Int. J. Impact Eng. 2017. Vol. 103. P. 76-89. https://doi.org/10.1016/j.ijimpeng.2017.01.009.
32. Wadi H. Imseeh, Khalid A.Alshibli. 3D finite element modelling of force transmission and particle fracture of sand. Comput. Geotech. 2018. Vol. 94. P. 184-195. https://doi.org/10.1016/j.compgeo.2017.09.008.
33. Linnik E.Yu., Kotov V.L., Konstantinov A.Yu. Sravnitelnyi analiz sil soprotivleniia vnedreniiu konicheskikh i piramidal'nykh tel v uprugoplasticheskuiu sredu [Сomparative analysis of resistance to the introduction of conical and pyramidal bodies to the elastic plastic environment]. Problemy prochnosti i plastichnosti [Problems of Strength and Plasticity]. 2017. Vol. 79. No 3. P. 338-347 (In Russian).
2. Park H., Chen W. Stress variations and particle movements during penetration into granular materials. T. Proulx (ed.). Dynamic Behavior of Materials, Conference Proceedings of the Society for Experimental Mechanics Series 99. 2011. Vol. 1. P. 85-92. https://doi.org/10.1007/978-1-4614-0216-9_11.
3. Collins A.L., Addiss J.W., Walley S.M., Promratana K., Bobaru F., Proud W.G., William-son D.M. The effect of rod nose shape on the internal flow fields during the ballistic penetration of sand. Int. J. Impact Eng. 2011. Vol. 38. Iss. 12. P. 951-963. https://doi.org/10.1016/j.ijimpeng.2011.08.002.
4. Savvateev A.F., Budin A.V., Kolikov V.A., Rutberg P.G. High-speed penetration into sand. Int. J. Impact Eng. 2001. Vol. 26. Iss. 1-10. P. 675-681. https://doi.org/10.1016/S0734-743X(01)00132-4.
5. Allen W.A., Mayfield E.B., Morrison H.L. Dynamics of a projectile penetrating sand. J. Appl. Phys. 1957. Vol. 28. No 3. P. 370-376.
6. Allen W.A., Mayfield E.B., Morrison H.L. Dynamics of a projectile penetrating sand. Part II. J. Appl. Phys. 1957. Vol. 28. Iss. 3. P. 1331-1335. https://doi.org/10.1063/1.1722750.
7. Veldanov V.A., Markov V.A., Pusev V.I., Ruchko A.M., Sotskii M.Yu., Fedorov S.V. Computation of non-deformable striker penetration into low strength obstacles using piezoelectric accelerometry data. Technical Physics. 2011. Vol. 56. No 7. P. 992-1002. https://doi.org/10.1134/S1063784211070231 .
8. Balandin Vl.V., Balandin Vl.Vl., Bragov A.M., Kotov V.L. Experimental study of the dynamics of penetration of a solid body into a soil medium. Technical Physics. 2016. Vol. 61. No 6. P. 860-868. https://doi.org/10.1134/S1063784216060037 .
9. Bivin Yu.K., Simonov I.V. Mechanics of dynamic penetration into soil medium. Mechanics of Solids. 2010. Vol. 45. Iss. 6. P. 892-920. https://doi.org/10.3103/S0025654410060130.
10. Forrestal M.J., Norwood F.R., Longcope D.B. Penetration into targets described by locked hydrostats and shear strength. Int. J. Solids Struct. 1981. Vol. 17. Iss. 9. P. 915-924. https://doi.org/10.1016/0020-7683(81)90106-2.
11. Omidvar M., Malioche J.D., Bless S., Iskander M. Phenomenology of rapid projectile penetra-tion into granular soils. Int. J. Impact Eng. 2015. Vol. 85. P. 146-160. https://doi.org/10.1016/j.ijimpeng.2015.06.002.
12. Ben-Dor G., Dubinsky A., Elperin T. Engineering models of high speed penetration into geological shields. Cent. Eur. J. Eng. 2014. Vol. 4. Iss. 1. P. 1-19. https://doi.org/10.2478/s13531-013-0135-4.
13. Kotov V.L., Balandin V.V., Bragov A.M., Linnik E.Yu., Balandin V.V. Using a local-interaction model to determine the resistance to penetration of projectiles into sandy soil. J. Appl. Mech. Tech. Phys. 2013. Vol. 54. Iss. 4. P. 612-621. https://doi.org/10.1134/S0021894413040123.
14. Cuncheng Shi, Mingyang Wang, Jie Li, Mengshen Li. A model of depth calculation for projectile penetration into dry sand and comparison with experiments. Int. J. Impact Eng. 2014. Vol. 73. P. 112-122. https://doi.org/10.1016/j.ijimpeng.2014.06.010.
15. Linnik E.Yu., Kotov V.L., Konstantinov A.Yu. Modelirovanie protsessov dinamicheskogo vnedreniya prostranstvennykh tel v szhimaemuyu uprugoplasticheskuyu sredu [Modeling the processes of dynamic penetration of dimensional bodies in a compressible elastoplastic medium]. Vestnik PNIPU. Mekhanika [PNRPU Mechanics Bulletin]. 2017. No 4. P. 92-108. DOI: 10.15593/perm.mech/2017.4.07 (In Russian).
16. Bazhenov V.G., Kotov V.L. Chislenno-analiticheskiy metod issledovaniya ustoychivosti dvizheniya tel vrashcheniya v myagkikh gruntovykh sredakh [Numerical-analytical method for investigation the stability of motion of bodies of rotation in soft soil media]. Prikladnaya matematika i mekhanika [J. Appl. Math. Mech.]. 2017. Vol. 81. No. 6. P. 688-698 (In Russian).
17. Aptukov V.N., Khasanov A.R. Optimizatsiya parametrov sloistykh plit pri dinamicheskom pronikanii zhestkogo indentora s uchetom treniya i oslablyayushchego effekta svobodnykh poverkh-nostey [Optimization of parameters of layered plates during dynamic hard indenter penetration with friction and weakining effect of free surfaces]. Vestnik PNIPU. Mekhanika [PNRPU Mechanics Bulletin]. 2014. No 2. P. 48-75. DOI: 10.15593/perm.mech/2014.2.03 (In Russian).
18. Ben-Dor G., Dubinsky A., Elperin T. Shape optimization of high-speed penetrators: a review. Cent. Eur. J. Eng. 2012. Vol. 2. No 4. P. 473-482. DOI: 10.2478/s13531-012-0022-4.
19. Bazhenov V.G., Balandin V.V., Grigoryan S.S., Kotov V.L. Analysis of models for calculating the motion of solids of revolution of minimum resistance in soil media. J. Appl. Math. Mech. 2014. Vol. 78. Iss. 1. P. 65-76. https://dx.doi.org/10.1016/j.jappmathmech.2014.05.008.
20. Kotov V.L., Linnik E.Yu. Study of motion of optimal bodies in the soil of grid method. 11th International Conference on Mesh Methods for Boundary-value Problems and Applications. 20–25 Oct. 2016. Kazan. 2016. P. 012058. DOI:10.1088/1757-899X/158/1/012058.
21. Bazhenov V.G., Kotov V.L., Krylov S.V., Balandin V.V., Bragov A.M., Tsvetkova E.V. Experimental-theoretical analysis of non-stationary interaction of deformable impactors with soil. J. Appl. Mech. Tech. Phys. 2001. Vol. 42. Iss. 6. P. 1083-1089. https://doi.org/10.1023/A:1012590517033.
22. Balandin V.V., Bragov A.M., Igumnov L.A., Konstantinov A.Yu., Kotov V.L., Lomunov A.K. Dynamic deformation of soft soil media: Experimental studies and mathematical modeling. Mecha-nics of Solids. 2015. Vol. 50. Iss. 3. P. 286-293. https://doi.org/10.3103/S002565441503005X.
23. Bazhenov V.G., Bragov A.M., Kotov V.L. Experimental-theoretical study of the penetration of rigid projectiles and identification of soil properties. J. Appl. Mech. Tech. Phys. 2009. Vol. 50. Iss. 6. P. 1011-1019. https://doi.org/10.1007/s10808-009-0135-6.
24. Bazhenov V.G., Bragov A.M., Kotov V.L., Kochetkov A.V. An investigation of the impact and penetration of solids of revolution into soft earth. J. Appl. Math. Mech. 2003. Vol. 67. Iss. 4. P. 611-620. https://doi.org/10.1016/S0021-8928(03)90064-5.
25. Grujicica M., Pandurangan B., Qiao R., Cheeseman B.A., Roy W.N., Skaggs R.R., Gupta R. Parameterization of the porous-material model for sand with different levels of water saturation. Soil Dynam. Earthquake Eng. 2008. Vol. 28. P. 20-35. https://doi.org/10.1016/j.soildyn.2007.05.001.
26. Bazhenov V.G., Kotov V.L., Kochetkov A.V., Krylov S.V., Feldgun V.R. Chislennoe modeli-rovanie nagruzheniya peschanogo grunta vzryvom nakladnogo zaryada [On wave processes in soil subjected to a surface charge explosion]. Izvestiya RAN. Mekhanika tverdogo tela [Mechanics of Solids]. 2001. Vol 36. Iss. 2. P. 62-68 (In Russian).
27. Borg J.P., Vogler T.J. Mesoscale simulations of a dart penetrating sand. Int. J. Impact Eng. 2008. Vol. 35. Iss. 12. P. 1435-1440. https://doi.org/10.1016/j.ijimpeng.2008.07.064.
28. Tran Q.A., Chevalier B., Breul P. Discrete modeling of penetration tests in constant velocity and impact conditions. Comput. Geotech. 2016. Vol. 71. P. 12-18. https://doi.org/10.1016/j.compgeo.2015.08.010.
29. Bo/rvik T., Dey S., Olovsson L. Penetration of granular materials by small-arms bullets. Int. J. Impact Eng. 2015. Vol. 75. P. 123-139. https://doi.org/10.1016/j.ijimpeng.2014.07.016.
30. Qin Fang, Jinhua Zhang, Yadong Zhang, Jinchun Liu. Mesoscopic investigation of the sand particulate system subjected to intense dynamic loadings. Int. J. Impact Eng. 2016. Vol. 89. P. 62-71. https://doi.org/10.1016/j.ijimpeng.2015.11.009.
31. Zhang L., Lambert S., Nicot F. Discrete dynamic modelling of the mechanical behaviour of a granular soil. Int. J. Impact Eng. 2017. Vol. 103. P. 76-89. https://doi.org/10.1016/j.ijimpeng.2017.01.009.
32. Wadi H. Imseeh, Khalid A.Alshibli. 3D finite element modelling of force transmission and particle fracture of sand. Comput. Geotech. 2018. Vol. 94. P. 184-195. https://doi.org/10.1016/j.compgeo.2017.09.008.
33. Linnik E.Yu., Kotov V.L., Konstantinov A.Yu. Sravnitelnyi analiz sil soprotivleniia vnedreniiu konicheskikh i piramidal'nykh tel v uprugoplasticheskuiu sredu [Сomparative analysis of resistance to the introduction of conical and pyramidal bodies to the elastic plastic environment]. Problemy prochnosti i plastichnosti [Problems of Strength and Plasticity]. 2017. Vol. 79. No 3. P. 338-347 (In Russian).
Опубликован
2018-12-15
Раздел
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