64
A. V. Demareva et al.
significant changes. The maximum value of the contact force F max does not exceed
900 kN. The impact time is approximately 22 ms, and average falling plate overload
equals to approximately 80 g.
In the active loading stage, the MHS filler computational model, MHS, allows
to determine the integral parameters of spherical shells buckling (contact forces,
displacements, displacement velocities) with an accuracy of up to 5% and to evaluate
their damping properties. When the plate rebounds, there is some discrepancy in the
results, which is explained by the complex behavior of the spherical shell at the
supercritical deformation stage. However, it should be taken into account that by this
time, 90% of the kinetic energy of the plate is already absorbed by the elastic–plastic
deformation of the shell.
4.4 Conclusion
Thus, the presented computational model with acceptable accuracy describes the
MHS filler nonlinear deformation. The MHS filler computational model stress–
strain diagram can be obtained on the basis of a numerical solution of the problem
of nonlinear deformation and spherical shell buckling under appropriate loading
conditions.
Acknowledgements The work is financially supported by the Federal Targeted Program for
Research and Development in Priority Areas of Development of the Russian Scientific and Technological Complex for 2014–2020 under the contract No. 075-15-2019-1702 (unique identifier
RFMEFI60519X0183).
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.
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.
Banhart, J. (2001). Manufacture, characterization and application of cellular metals and metal foams.
Progress in Materials Science., 46, 559–632.
Barchiesi, E., Spagnuolo, M., & Placidi, L. (2018) Mechanical metamaterials: A state of the art.
Mathematics and Mechanics of Solids.
Bathe, K. Y. (1996). Finite element procedures. Upper Saddle River, NJ: «Prentice Hall» 1037p.
Baumeister, J., & Banhart, J. (1998). Deformation characteristics of metal foam. Journal of
Materials Science, 33, 1431–1440.
Bazhenov, V. G., Kibets, A. I., & Tsvetkova, I. N. (1995). Numerical simulation of transient processes
of shock interaction of deformable elements of constructions. Problemy Mashinostroeniia I
Nadezhnosti Mashin, 2, 20–26.
A. V. Demareva et al.
significant changes. The maximum value of the contact force F max does not exceed
900 kN. The impact time is approximately 22 ms, and average falling plate overload
equals to approximately 80 g.
In the active loading stage, the MHS filler computational model, MHS, allows
to determine the integral parameters of spherical shells buckling (contact forces,
displacements, displacement velocities) with an accuracy of up to 5% and to evaluate
their damping properties. When the plate rebounds, there is some discrepancy in the
results, which is explained by the complex behavior of the spherical shell at the
supercritical deformation stage. However, it should be taken into account that by this
time, 90% of the kinetic energy of the plate is already absorbed by the elastic–plastic
deformation of the shell.
4.4 Conclusion
Thus, the presented computational model with acceptable accuracy describes the
MHS filler nonlinear deformation. The MHS filler computational model stress–
strain diagram can be obtained on the basis of a numerical solution of the problem
of nonlinear deformation and spherical shell buckling under appropriate loading
conditions.
Acknowledgements The work is financially supported by the Federal Targeted Program for
Research and Development in Priority Areas of Development of the Russian Scientific and Technological Complex for 2014–2020 under the contract No. 075-15-2019-1702 (unique identifier
RFMEFI60519X0183).
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.
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.
Banhart, J. (2001). Manufacture, characterization and application of cellular metals and metal foams.
Progress in Materials Science., 46, 559–632.
Barchiesi, E., Spagnuolo, M., & Placidi, L. (2018) Mechanical metamaterials: A state of the art.
Mathematics and Mechanics of Solids.
Bathe, K. Y. (1996). Finite element procedures. Upper Saddle River, NJ: «Prentice Hall» 1037p.
Baumeister, J., & Banhart, J. (1998). Deformation characteristics of metal foam. Journal of
Materials Science, 33, 1431–1440.
Bazhenov, V. G., Kibets, A. I., & Tsvetkova, I. N. (1995). Numerical simulation of transient processes
of shock interaction of deformable elements of constructions. Problemy Mashinostroeniia I
Nadezhnosti Mashin, 2, 20–26.