188
L. Igumnov et al.
Acknowledgements This work was supported by a grant of the Russian Science Foundation (1619-10237-P).
References
Alibert J.J., Seppecher P., dell’Isola F. Truss modular beams with deformation energy depending
on higher displacement gradients. Mathematics and Mechanics of Solids, 2003, 8(1)
Arkhangelskiy A. Ya. C++Builder 6. Spravochnoe posobiye. M.:Binom-Press, 2002. – p.544 (in
Russian).
Auffray N., dell’Isola F., Eremeyev V., Madeo A., Rossi G. Analytical continuum mechanics
à la Hamilton-Piola: least action principle for second gradient continua and capillary fluids.
Mathematics and Mechanics of Solids, 2013
Babitskiy V. I., Krupenin V. L. Oscillations in Strongly Nonlinear Systems. Science, 1985, p. 320,
(in Russian).
Babitsky, V. I. (1998). Theory of Vibro-Impact Systems. New York: Springer. ((in Russian)).
Babitsky, V. I. Theory of Vibro-impact Systems and Applications, Springer Science & Business
Media, 2013.
Bakhvalov N.S., Zhidkov N.P., Kobelkov G.M. Numerical methods. Binom. Laboratoriya znaniy,
2003 – p. 640 (in Russian).
Barchiesi, E., Spagnuolo, M., & Placidi, L. (2018). Mechanical metamaterials: A state of the art.
Mathematics and Mechanics of Solids.
Bernardini D., & Litak, G. An overview of 0–1 test for chaos, Journal of the Brazilian Society of
Mechanical Sciences and Engineering, vol. 38, no. 5. 2016, p. 1433–1450.
Biderman V. L. The Applied Theory of Mechanical Oscillations. High School, 1972, p. 416, (in
Russian).
Bogodukhov S. I., Grebenyuk V. F., Proskurin A. D. Processing of strengthened surfaces in
mechanical engineering a maintenance. Mechanical Engineering, 2005, p. 256, (in Russian).
Cveticanin, L. (2002). The motion of a two-mass system with non-linear connection. Journal of
Sound and Vibration, 252(2), 361–369.
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.
dell’Isola F., Andreaus U, Placidi L. 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, 2015, 20(8)
dell’Isola F., Cuomo M., Greco L., Della Corte A. Bias extension test for pantographic sheets: numerical simulations based on second gradient shear energies. Journal of Engineering Mathematics,
2017
dell’Isola, F., Della, C. A., & Giorgio, I. (2016). Higher-gradient continua: The legacy of Piola,
Mindlin. Mathematics and Mechanics of Solids: Sedov and Toupin and some future research
perspectives.
dell’Isola F., Della Corte A., Greco L., Luongo A. Plane bias extension test for a continuum with two
inextensible families of fibers: a variational treatment with Lagrange multipliers and a perturbation
solution. International Journal of Solids and Structures, 2016
dell’Isola F., Giorgio I., Pawlikowski M., Rizzi N. Large deformations of planar extensible beams
and pantographic lattices: heuristic homogenization, experimental and numerical examples of
equilibrium. Proceedings of The Royal Society A, 2016, 472(2185)
dell’Isola, F., Seppecher, P., & Alibert, J. J. (2019). Pantographic metamaterials: An example of
mathematically driven design and of its technological challenges. Continuum Mechanics and
Thermodynamics, 31(4), 851–884.
L. Igumnov et al.
Acknowledgements This work was supported by a grant of the Russian Science Foundation (1619-10237-P).
References
Alibert J.J., Seppecher P., dell’Isola F. Truss modular beams with deformation energy depending
on higher displacement gradients. Mathematics and Mechanics of Solids, 2003, 8(1)
Arkhangelskiy A. Ya. C++Builder 6. Spravochnoe posobiye. M.:Binom-Press, 2002. – p.544 (in
Russian).
Auffray N., dell’Isola F., Eremeyev V., Madeo A., Rossi G. Analytical continuum mechanics
à la Hamilton-Piola: least action principle for second gradient continua and capillary fluids.
Mathematics and Mechanics of Solids, 2013
Babitskiy V. I., Krupenin V. L. Oscillations in Strongly Nonlinear Systems. Science, 1985, p. 320,
(in Russian).
Babitsky, V. I. (1998). Theory of Vibro-Impact Systems. New York: Springer. ((in Russian)).
Babitsky, V. I. Theory of Vibro-impact Systems and Applications, Springer Science & Business
Media, 2013.
Bakhvalov N.S., Zhidkov N.P., Kobelkov G.M. Numerical methods. Binom. Laboratoriya znaniy,
2003 – p. 640 (in Russian).
Barchiesi, E., Spagnuolo, M., & Placidi, L. (2018). Mechanical metamaterials: A state of the art.
Mathematics and Mechanics of Solids.
Bernardini D., & Litak, G. An overview of 0–1 test for chaos, Journal of the Brazilian Society of
Mechanical Sciences and Engineering, vol. 38, no. 5. 2016, p. 1433–1450.
Biderman V. L. The Applied Theory of Mechanical Oscillations. High School, 1972, p. 416, (in
Russian).
Bogodukhov S. I., Grebenyuk V. F., Proskurin A. D. Processing of strengthened surfaces in
mechanical engineering a maintenance. Mechanical Engineering, 2005, p. 256, (in Russian).
Cveticanin, L. (2002). The motion of a two-mass system with non-linear connection. Journal of
Sound and Vibration, 252(2), 361–369.
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.
dell’Isola F., Andreaus U, Placidi L. 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, 2015, 20(8)
dell’Isola F., Cuomo M., Greco L., Della Corte A. Bias extension test for pantographic sheets: numerical simulations based on second gradient shear energies. Journal of Engineering Mathematics,
2017
dell’Isola, F., Della, C. A., & Giorgio, I. (2016). Higher-gradient continua: The legacy of Piola,
Mindlin. Mathematics and Mechanics of Solids: Sedov and Toupin and some future research
perspectives.
dell’Isola F., Della Corte A., Greco L., Luongo A. Plane bias extension test for a continuum with two
inextensible families of fibers: a variational treatment with Lagrange multipliers and a perturbation
solution. International Journal of Solids and Structures, 2016
dell’Isola F., Giorgio I., Pawlikowski M., Rizzi N. Large deformations of planar extensible beams
and pantographic lattices: heuristic homogenization, experimental and numerical examples of
equilibrium. Proceedings of The Royal Society A, 2016, 472(2185)
dell’Isola, F., Seppecher, P., & Alibert, J. J. (2019). Pantographic metamaterials: An example of
mathematically driven design and of its technological challenges. Continuum Mechanics and
Thermodynamics, 31(4), 851–884.