4 Finite Element Method Study of the Protection …
65
Bazhenov, V. G., Gonik, E. G., Kibets, A. I., & Shoshin, D. V. (2014). Stability and limit states
of elastoplastic spherical shells under static and dynamic loading. Journal of Applied Mechanics
and Technical Physics, 55(1), 8–15.
Bazhenov, V. G., Demareva, A. V., Zhestkov, M. N., & Kibets, A. I. (2016a). Special features of
numerical simulation for elastic-plastic buckling of hemispherical shells under loading with the
rigid indenter. PNRPU Mechanics Bulletin, 2, 22–33.
Bazhenov, V. G., Demareva, A. V., Baranova, M. S., Kibets, A. I., Ryabov, A. A., & Romanov, V.
I. (2016b). Finite-element modeling of large elastoplastic deformations of a spherical shell in a
scaphander under an overload pulse. Problems of Strenght and Plasticity, 78(3), 322–332.
Caty, O., Maire, E., Douillard, T., Bertino, P., Dejaeger, R., & Bouchet, R. (2009). Experimental
determination of the macroscopic fatigue properties of metal hollow sphere structures. Materials
Letters, 63, 1131–1134.
Davies, G. J., & Zhen, S. (1983). Metallic foams-their production, properties and applications.
Journal of Materials Science, 18(7), 1899–1911.
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, 63, 1119–1141.
dell’Isola, F., Della, C. 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.
dell’Isola, F., & Batra, R. (1997). Saint-Venant’s problem for porous linear elastic materials. Journal
of Elasticity, 47(1).
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).
dell’Isola, F., Madeo, A., & Seppecher, P. (2009). Boundary conditions at fluid-permeable interfaces
in porous media: A variational approach. International Journal of Solids and Structures, 246(17).
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.
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.
Demareva, A. V., Ivanov, V. A., Zhestkov, M. N., Kibets, A. I., Kibets, Yu. I., & Shoshin, D. V.
(2014). Numerically analyzing dynamic problems of deformation of multilayered shells with a
porous filling. Problems of Strenght and Plasticity, 76(1), 46–54.
Gibson, L. J., & Ashby, M. F. (1997). Cellular solids: Structure and properties (p. 528). Cambridge:
Cambridge University Press.
Giorgio, I. (2016). Numerical identification procedure between a micro-Cauchy model and a macrosecond gradient model for planar pantographic structures. Zeitschrift für an-gewandte Mathematik
und Physik.
Golovanov, A. I., Tiuleneva, O. N., & Shigabutdinov, A. F. (2006). The finite element method in
statics and dynamics of thin-walled structures (p. 391). Moscow: Fizmatlit.
Hallquist, J. O. (1998). LS-DYNA: Theoretical manual (p. 498p). Livermore: Livermore Software
Technology Corporation.
Liu YB, Wu HX, Wang B (2012) Gradient design of metal hollow sphere (MHS) foams with density
gradients. Composites Part B: Engineering 43, 1346–1352.
Madeo, A., dell’Isola, F., & Darve, F. (2013). A continuum model for deformable, second gradient
porous media partially saturated with compressible fluids. Journal of the Mechanics and Physics
of Solids, 61(11).
65
Bazhenov, V. G., Gonik, E. G., Kibets, A. I., & Shoshin, D. V. (2014). Stability and limit states
of elastoplastic spherical shells under static and dynamic loading. Journal of Applied Mechanics
and Technical Physics, 55(1), 8–15.
Bazhenov, V. G., Demareva, A. V., Zhestkov, M. N., & Kibets, A. I. (2016a). Special features of
numerical simulation for elastic-plastic buckling of hemispherical shells under loading with the
rigid indenter. PNRPU Mechanics Bulletin, 2, 22–33.
Bazhenov, V. G., Demareva, A. V., Baranova, M. S., Kibets, A. I., Ryabov, A. A., & Romanov, V.
I. (2016b). Finite-element modeling of large elastoplastic deformations of a spherical shell in a
scaphander under an overload pulse. Problems of Strenght and Plasticity, 78(3), 322–332.
Caty, O., Maire, E., Douillard, T., Bertino, P., Dejaeger, R., & Bouchet, R. (2009). Experimental
determination of the macroscopic fatigue properties of metal hollow sphere structures. Materials
Letters, 63, 1131–1134.
Davies, G. J., & Zhen, S. (1983). Metallic foams-their production, properties and applications.
Journal of Materials Science, 18(7), 1899–1911.
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, 63, 1119–1141.
dell’Isola, F., Della, C. 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.
dell’Isola, F., & Batra, R. (1997). Saint-Venant’s problem for porous linear elastic materials. Journal
of Elasticity, 47(1).
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).
dell’Isola, F., Madeo, A., & Seppecher, P. (2009). Boundary conditions at fluid-permeable interfaces
in porous media: A variational approach. International Journal of Solids and Structures, 246(17).
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.
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.
Demareva, A. V., Ivanov, V. A., Zhestkov, M. N., Kibets, A. I., Kibets, Yu. I., & Shoshin, D. V.
(2014). Numerically analyzing dynamic problems of deformation of multilayered shells with a
porous filling. Problems of Strenght and Plasticity, 76(1), 46–54.
Gibson, L. J., & Ashby, M. F. (1997). Cellular solids: Structure and properties (p. 528). Cambridge:
Cambridge University Press.
Giorgio, I. (2016). Numerical identification procedure between a micro-Cauchy model and a macrosecond gradient model for planar pantographic structures. Zeitschrift für an-gewandte Mathematik
und Physik.
Golovanov, A. I., Tiuleneva, O. N., & Shigabutdinov, A. F. (2006). The finite element method in
statics and dynamics of thin-walled structures (p. 391). Moscow: Fizmatlit.
Hallquist, J. O. (1998). LS-DYNA: Theoretical manual (p. 498p). Livermore: Livermore Software
Technology Corporation.
Liu YB, Wu HX, Wang B (2012) Gradient design of metal hollow sphere (MHS) foams with density
gradients. Composites Part B: Engineering 43, 1346–1352.
Madeo, A., dell’Isola, F., & Darve, F. (2013). A continuum model for deformable, second gradient
porous media partially saturated with compressible fluids. Journal of the Mechanics and Physics
of Solids, 61(11).