86
V. L. Kotov et al.
dell’Isola, F., Della Corte, A., & Giorgio, I. (2017). Higher-gradient continua: The legacy of Pio-la,
Mindlin, Sedov and Toupin and some future research perspectives. Mathematics and Mechanics
of Solids, 22, 852–872.
dell’Isola, F., Seppecher, P., Alibert, J. J., Lekszycki, T., Grygoruk, R., Pawlikowski, M., et al.
(2019). Pantographic metamaterials: An example of mathematically driven design and of its
technological challenges. Continuum Mechanics and Thermodynamics, 31(4), 851–884.
Del Vescovo, D., & Giorgio, I. (2014). Dynamic problems for metamaterials: Review of existing
models and ideas for further research. International Journal of Engineering Science, 80, 153–172.
Dianov, M. D., Zlatin, N. A., Mochalov, S. M., et al. (1977). Shock compressibility of dry and
water-saturated sand. Soviet Technical Physics Letters, 2, 207–208.
Forrestal, M. J., & Longcope, D. B. (1982). Closed-form solution for forces on conical-nosed
penetrators into geological targets with constant shear strength. Mechanics of Materials, 1, 285–
295.
Forrestal, M. J., & Luk, V. K. (1988). Dynamic spherical cavity-expansion in a compressible elasticplastic solid. The Journal of Applied Mechanics, 55(2), 275–279 https://doi.org/10.1115/1.317
3672.
Forrestal, M. J., & Luk, V. K. (1992). Penetration into soil targets. The International Journal of
Impact Engineering, 12(3), 427–444. https://doi.org/10.1016/0734-743X(92)90167-R.
Grigoryan, S. S. (1960). On basic concepts of soil dynamics. Journal of Applied Mathematics and
Mechanics, 24(6), 1604–1627. https://doi.org/10.1016/0021-8928(60)90013-7.
Kong, X. Z., Wu, H., Fang, Q., & Peng, Y. (2017). Rigid and eroding projectile penetration into
concrete targets based on an extended dynamic cavity expansion model. The International Journal
of Impact Engineering, 100, 13–22.
Kotov, V. L. (2008). Studying the applicability of the auto-modeling analysis of the problem of
expansion of a spherical cavity in a compressible medium for determining the pressure on the
surface of the striker-soil contact. Problems of Strength and Plasticity, 70, 123–131. (in Russian).
Kotov, V. L. (2019). Approximation of stresses in the vicinity of the cavity, expanding at a constant
speed in a medium with the Mohr-Coulomb yield criterion. Problems of Strength and Plasticity,
81(2), 1–10. (in Russian).
Kotov, V. L., Linnik, E. Yu., Tarasova, A. A., & Makarova, A. A. (2011). The analysis of approximate
solutions of a spherical cavity expansion in a soil medium problem. Problems of Strength and
Plasticity, 73, 58–63. (in Russian).
Kotov, V. L., Balandin, V. V., Bragov, A. M., Linnik, E. Yu., & Balandin, V. V. (2013). Using a
local-interaction model to determine the resistance to penetration of projectiles into sandy soil.
Journal of Applied Mechanics and Technical Physics, 54(4), 612–621 https://doi.org/10.1134/
S0021894413040123.
Lagunov, V. A., & Stepanov, V. A. (1963). Measurements of the dynamic compressibility of sand
under high pressures. Zh. Prikl. Mekh. Tekhn. Fiz., 1, 88–96. [J. Appl. Mech. Tech. Phys. (Engl.
Transl.)].
Linnik, E. Yu., Kotov, V. L., Tarasova, A. A., & Gonik, E. G. (2012). The solution of the problem
of the expansion of a spherical cavity in a soil medium assuming incompressibility beyond the
shock front. Problems of Strength and Plasticity., 74, 49–58. (In Russian).
Omidvar, M., Iskander, M., & Bless, S. (2012). Stress-strain behavior of sand at high strain rates.
International Journal of Impact Engineering, 49, 192–213. https://doi.org/10.1016/j.ijimpeng.
2012.03.004.
Omidvar, M., Iskander, M., & Bless, S. (2014). Response of granular media to rapid penetration.
International Journal of Impact Engineering, 66, 60–82. https://doi.org/10.1016/j.ijimpeng.2013.
12.004.
Omidvar, M., Malioche, Jeanne D., Bless, S., & Iskander, M. (2015). Phenomenology of rapid
projectile penetration into granular soils. International Journal of Impact Engineering, 85, 146–
160. https://doi.org/10.1016/j.ijimpeng.2015.06.002.
Placidi, L., Barchiesi, E., Turco, E., & Rizzi, N. L. (2016). A review on 2D models for the description
of pantographic fabrics. Zeitschrift für angewandte Mathematik und Physik, 67(5).
V. L. Kotov et al.
dell’Isola, F., Della Corte, A., & Giorgio, I. (2017). Higher-gradient continua: The legacy of Pio-la,
Mindlin, Sedov and Toupin and some future research perspectives. Mathematics and Mechanics
of Solids, 22, 852–872.
dell’Isola, F., Seppecher, P., Alibert, J. J., Lekszycki, T., Grygoruk, R., Pawlikowski, M., et al.
(2019). Pantographic metamaterials: An example of mathematically driven design and of its
technological challenges. Continuum Mechanics and Thermodynamics, 31(4), 851–884.
Del Vescovo, D., & Giorgio, I. (2014). Dynamic problems for metamaterials: Review of existing
models and ideas for further research. International Journal of Engineering Science, 80, 153–172.
Dianov, M. D., Zlatin, N. A., Mochalov, S. M., et al. (1977). Shock compressibility of dry and
water-saturated sand. Soviet Technical Physics Letters, 2, 207–208.
Forrestal, M. J., & Longcope, D. B. (1982). Closed-form solution for forces on conical-nosed
penetrators into geological targets with constant shear strength. Mechanics of Materials, 1, 285–
295.
Forrestal, M. J., & Luk, V. K. (1988). Dynamic spherical cavity-expansion in a compressible elasticplastic solid. The Journal of Applied Mechanics, 55(2), 275–279 https://doi.org/10.1115/1.317
3672.
Forrestal, M. J., & Luk, V. K. (1992). Penetration into soil targets. The International Journal of
Impact Engineering, 12(3), 427–444. https://doi.org/10.1016/0734-743X(92)90167-R.
Grigoryan, S. S. (1960). On basic concepts of soil dynamics. Journal of Applied Mathematics and
Mechanics, 24(6), 1604–1627. https://doi.org/10.1016/0021-8928(60)90013-7.
Kong, X. Z., Wu, H., Fang, Q., & Peng, Y. (2017). Rigid and eroding projectile penetration into
concrete targets based on an extended dynamic cavity expansion model. The International Journal
of Impact Engineering, 100, 13–22.
Kotov, V. L. (2008). Studying the applicability of the auto-modeling analysis of the problem of
expansion of a spherical cavity in a compressible medium for determining the pressure on the
surface of the striker-soil contact. Problems of Strength and Plasticity, 70, 123–131. (in Russian).
Kotov, V. L. (2019). Approximation of stresses in the vicinity of the cavity, expanding at a constant
speed in a medium with the Mohr-Coulomb yield criterion. Problems of Strength and Plasticity,
81(2), 1–10. (in Russian).
Kotov, V. L., Linnik, E. Yu., Tarasova, A. A., & Makarova, A. A. (2011). The analysis of approximate
solutions of a spherical cavity expansion in a soil medium problem. Problems of Strength and
Plasticity, 73, 58–63. (in Russian).
Kotov, V. L., Balandin, V. V., Bragov, A. M., Linnik, E. Yu., & Balandin, V. V. (2013). Using a
local-interaction model to determine the resistance to penetration of projectiles into sandy soil.
Journal of Applied Mechanics and Technical Physics, 54(4), 612–621 https://doi.org/10.1134/
S0021894413040123.
Lagunov, V. A., & Stepanov, V. A. (1963). Measurements of the dynamic compressibility of sand
under high pressures. Zh. Prikl. Mekh. Tekhn. Fiz., 1, 88–96. [J. Appl. Mech. Tech. Phys. (Engl.
Transl.)].
Linnik, E. Yu., Kotov, V. L., Tarasova, A. A., & Gonik, E. G. (2012). The solution of the problem
of the expansion of a spherical cavity in a soil medium assuming incompressibility beyond the
shock front. Problems of Strength and Plasticity., 74, 49–58. (In Russian).
Omidvar, M., Iskander, M., & Bless, S. (2012). Stress-strain behavior of sand at high strain rates.
International Journal of Impact Engineering, 49, 192–213. https://doi.org/10.1016/j.ijimpeng.
2012.03.004.
Omidvar, M., Iskander, M., & Bless, S. (2014). Response of granular media to rapid penetration.
International Journal of Impact Engineering, 66, 60–82. https://doi.org/10.1016/j.ijimpeng.2013.
12.004.
Omidvar, M., Malioche, Jeanne D., Bless, S., & Iskander, M. (2015). Phenomenology of rapid
projectile penetration into granular soils. International Journal of Impact Engineering, 85, 146–
160. https://doi.org/10.1016/j.ijimpeng.2015.06.002.
Placidi, L., Barchiesi, E., Turco, E., & Rizzi, N. L. (2016). A review on 2D models for the description
of pantographic fabrics. Zeitschrift für angewandte Mathematik und Physik, 67(5).