5 Analyzing the Problem of a Spherical Cavity Expansion …
85
References
Abali, B. E., Muller, W., & dell’Isola, F. (2017). Theory and computation of higher gradient elasticity
theories based on action principles. Archive of Applied Mechanics, 87, 1495–1510.
Alibert, J. J., Seppecher, P., & dell’Isola, F. (2003). Truss modular beams with deformation energy
depending on higher displacement gradients. Mathematics and Mechanics of Solids, 8, 51–73.
Arlery, M., Gardou, M., Fleureau, J. M., & Mariotti, C. (2010). Dynamic behaviour of dry and watersaturated sand under planar shock conditions. The International Journal of Impact Engineering,
37, 1–10. https://doi.org/10.1016/j.ijimpeng.2009.07.009.
Auffray, N., dell’Isola, F., Eremeyev, V., Madeo, A., & Rosi, G. (2013). Analytical continuum
mechanics à la Hamilton-Piola: Least action principle for second gradient continua and capillary
fluids. Mathematics and Mechanics of Solids.
Balandin, V. V., Bragov, A. M., Igumnov, L. A., Konstantinov, A. Yu., Kotov, V. L., & Lomunov,
A. K. (2015). Dynamic deformation of soft soil media: Experimental studies and mathematical
modeling. Mechanics of Solids, 50(3), 286–293. https://doi.org/10.3103/S002565441503005X.
Barchiesi, E., Spagnuolo, M., & Placidi, L. (2018). Mechanical metamaterials: A state of the art.
Mathematics and Mechanics of Solids.
Bazhenov, V. G., & Kotov, V. L. (2008). Method for identifying elastoplastic properties of ground
media by penetration of impactors. Mechanics of Solids, 4(43), 678–686. https://doi.org/10.3103/
S002565440804016X.
Bazhenov, V. G., Kotov, V. L., Kochetkov, A. V., Krylov, S. V., & Feldgun, V. R. (2001). On wave
processes in soil subjected to a surface charge explosion. Mechanics of Solids, 2(36), 62–68.
Bazhenov, V. G., Bragov, A. M., & Kotov, V. L. (2009). Experimental-theoretical study of the
penetration of rigid projectiles and identification of soil properties. Journal of Applied Mechanics
and Technical Physics, 6(50), 1011–1019. https://doi.org/10.1007/s10808-009-0135-6.
Ben-Dor, G., Dubinsky, A., & Elperin, T. (2005). Ballistic impact: Recent advances in analytical
modeling of plate penetration dynamics–A review. Applied Mechanics Reviews, 58, 355–371.
Bragov, A. M., & Grushevskii, G. M. (1993). Influence of the moisture content and granulometric
composition on the shock compressibility of sand. Technical Physics Letters, 19, 385–386.
Bragov, A. M., Lomunov, A. K., Sergeichev, I. V., Proud, W., Tsembelis, K., & Church, P. (2005).
A method for determining the main mechanical properties of soft soils at high strain rates (103–
105 s–1) and load amplitudes up to several gigapascals. Technical Physics Letters, 31(6), 530–531.
https://doi.org/10.1134/1.1969791.
Bragov, A. M., Balandin, V. V., Igumnov, L. A., Kotov, V. L., Krushka, L., & Lomunov, A. K. (2018).
Impact and penetration of cylindrical bodies into dry and water-saturated sand. International
Journal of Impact Engineering, 122, 197–208.
dell’Isola, F., & Hutter, K. (1998). A qualitative analysis of the dynamics of a sheared and pressurized
layer of saturated soil. Proceedings of the Royal Society of London A: Mathematical, Physical
and Engineering Sciences, 454(1980), 3105–3120.
dell’Isola, F., & Hutter, K. (1999). Variations of porosity in a sheared pressurized layer of saturated soil induced by vertical drainage of water. Proceedings of the Royal Society of London A:
Mathematical, Physical and Engineering Sciences, 455(1988), 2841–2860.
dell’Isola, F., Guarascio, M., & Hutter, K. (2000). A variational approach for the deformation of a
saturated porous solid. A second-gradient theory extending Terzaghi’s effective stress principle.
Archive of Applied Mechanics, 70(5), 323–337.
dell’Isola, F., Seppecher, P., & Madeo, A. (2012). How contact interactions may depend on the
shape of Cauchy cuts in Nth gradient continua: Approach “à la D’Alembert”. Zeitschrift für
Angewandte Mathematik und Physik (ZAMP), 63(6), 1119–1141.
dell’Isola, F., Andreaus, U., & Placidi, L. (2015). At the origins and in the vanguard of peridynamics, non-local and higher gradient continuum mechanics. An underestimated and still
topical contribution of Gabrio Piola. Mathematics and Mechanics of Solids, 20, 887–928.
dell’Isola, F., Madeo, A., & Seppecher, P. (2016). Cauchy tetrahedron argument applied to higher
contact interactions. Archive for Rational Mechanics and Analysis, 219(3).
85
References
Abali, B. E., Muller, W., & dell’Isola, F. (2017). Theory and computation of higher gradient elasticity
theories based on action principles. Archive of Applied Mechanics, 87, 1495–1510.
Alibert, J. J., Seppecher, P., & dell’Isola, F. (2003). Truss modular beams with deformation energy
depending on higher displacement gradients. Mathematics and Mechanics of Solids, 8, 51–73.
Arlery, M., Gardou, M., Fleureau, J. M., & Mariotti, C. (2010). Dynamic behaviour of dry and watersaturated sand under planar shock conditions. The International Journal of Impact Engineering,
37, 1–10. https://doi.org/10.1016/j.ijimpeng.2009.07.009.
Auffray, N., dell’Isola, F., Eremeyev, V., Madeo, A., & Rosi, G. (2013). Analytical continuum
mechanics à la Hamilton-Piola: Least action principle for second gradient continua and capillary
fluids. Mathematics and Mechanics of Solids.
Balandin, V. V., Bragov, A. M., Igumnov, L. A., Konstantinov, A. Yu., Kotov, V. L., & Lomunov,
A. K. (2015). Dynamic deformation of soft soil media: Experimental studies and mathematical
modeling. Mechanics of Solids, 50(3), 286–293. https://doi.org/10.3103/S002565441503005X.
Barchiesi, E., Spagnuolo, M., & Placidi, L. (2018). Mechanical metamaterials: A state of the art.
Mathematics and Mechanics of Solids.
Bazhenov, V. G., & Kotov, V. L. (2008). Method for identifying elastoplastic properties of ground
media by penetration of impactors. Mechanics of Solids, 4(43), 678–686. https://doi.org/10.3103/
S002565440804016X.
Bazhenov, V. G., Kotov, V. L., Kochetkov, A. V., Krylov, S. V., & Feldgun, V. R. (2001). On wave
processes in soil subjected to a surface charge explosion. Mechanics of Solids, 2(36), 62–68.
Bazhenov, V. G., Bragov, A. M., & Kotov, V. L. (2009). Experimental-theoretical study of the
penetration of rigid projectiles and identification of soil properties. Journal of Applied Mechanics
and Technical Physics, 6(50), 1011–1019. https://doi.org/10.1007/s10808-009-0135-6.
Ben-Dor, G., Dubinsky, A., & Elperin, T. (2005). Ballistic impact: Recent advances in analytical
modeling of plate penetration dynamics–A review. Applied Mechanics Reviews, 58, 355–371.
Bragov, A. M., & Grushevskii, G. M. (1993). Influence of the moisture content and granulometric
composition on the shock compressibility of sand. Technical Physics Letters, 19, 385–386.
Bragov, A. M., Lomunov, A. K., Sergeichev, I. V., Proud, W., Tsembelis, K., & Church, P. (2005).
A method for determining the main mechanical properties of soft soils at high strain rates (103–
105 s–1) and load amplitudes up to several gigapascals. Technical Physics Letters, 31(6), 530–531.
https://doi.org/10.1134/1.1969791.
Bragov, A. M., Balandin, V. V., Igumnov, L. A., Kotov, V. L., Krushka, L., & Lomunov, A. K. (2018).
Impact and penetration of cylindrical bodies into dry and water-saturated sand. International
Journal of Impact Engineering, 122, 197–208.
dell’Isola, F., & Hutter, K. (1998). A qualitative analysis of the dynamics of a sheared and pressurized
layer of saturated soil. Proceedings of the Royal Society of London A: Mathematical, Physical
and Engineering Sciences, 454(1980), 3105–3120.
dell’Isola, F., & Hutter, K. (1999). Variations of porosity in a sheared pressurized layer of saturated soil induced by vertical drainage of water. Proceedings of the Royal Society of London A:
Mathematical, Physical and Engineering Sciences, 455(1988), 2841–2860.
dell’Isola, F., Guarascio, M., & Hutter, K. (2000). A variational approach for the deformation of a
saturated porous solid. A second-gradient theory extending Terzaghi’s effective stress principle.
Archive of Applied Mechanics, 70(5), 323–337.
dell’Isola, F., Seppecher, P., & Madeo, A. (2012). How contact interactions may depend on the
shape of Cauchy cuts in Nth gradient continua: Approach “à la D’Alembert”. Zeitschrift für
Angewandte Mathematik und Physik (ZAMP), 63(6), 1119–1141.
dell’Isola, F., Andreaus, U., & Placidi, L. (2015). At the origins and in the vanguard of peridynamics, non-local and higher gradient continuum mechanics. An underestimated and still
topical contribution of Gabrio Piola. Mathematics and Mechanics of Solids, 20, 887–928.
dell’Isola, F., Madeo, A., & Seppecher, P. (2016). Cauchy tetrahedron argument applied to higher
contact interactions. Archive for Rational Mechanics and Analysis, 219(3).