Abstract
The present article deals with a solution of an analogue of the Prandtl problem on compression and drain (spreading) of a perfectly rigid plastic material in an asymptotically thin spherical layer by taking into account inertial effects. Various compression modes that characterize the transition from a quasistatic process to a dynamic one are considered.
Similar content being viewed by others
REFERENCES
L. Prandtl, “Anwendungsbeispiele zu einem henckyschen Satz uber das plastiche Gleichgewicht,” ZAMM 3 (6), 401–406 (1923).
A. Nadai, Theory of Flow and Fracture of Solids (Wiley, New York, 1950).
R. Hill, The Mathematical Theory of Plasticity (Clarendon Press, Oxford, 1950).
I. A. Kiiko, “The action of a compressed thin plastic layer on elastic surfaces,” Izv. Akad. Nauk SSSR, Otd. Tekh. Nauk, Mekh. Mashinostr., No. 6 1082–1085 (1961).
B. E. Pobedrya and I. L. Guzei, “Mathematical modeling of deformation of composites with the thermal diffusion being taken into account,” Matem. Modelir. Sist. Prots., No. 6, pp. 82–91 (1998).
I. A. Kiiko, “A generalization of Prandtl’s problem on contraction of a strip to the case of compressible materials,” Moscow Univ. Mech. Bull. 57 (4), 22–26 (2002).
A. A. Il’yushin, Collected Works, Vol. 4: Modeling of Dynamic Processes in Solids and Engineering Applications (Fizmatlit, Moscow, 2009) [in Russian].
G. I. Bykovtsev, “on compression of a plastic layer by rigid rough plates with forces of inertia taken into account,” Izv. Akad. Nauk SSSR. OTN. Mekh. Mashinostr., No. 6, 140–142 (1960).
I. A. Kiiko and B. A. Kadymov, “Generalization of the Prandtl problem on the compression of a strip,” Moscow Univ. Mech. Bull. 58 (4), 31–36 (2003).
D. V. Georgievskii, “Asymptotic Integration of the Prandtl problem in dynamic statement,” Mech. Solids 48 (1), 79–85 (2013).
D. V. Georgievskii and R. R. Shabaykin, “Quasistatic and dynamic compression of a plane perfectly plastic circular layer by rigid plates” in Mathematical Modeling and Experimental Mechanics of Deformable Solids, Ed. by V. G. Zubchaninov and A.A. Alekseev (Izd-vo TverGTU, Tver’, 2017), pp. 56–63.
M. A. Zadoyan, Spatial Problems of Plasticity Theory (Nauka, Moscow, 1992) [in Russian].
A. Yu. Ishlinskii and D. D. Ivlev, The Mathematical Theory of Plasticity (Fizmatlit, Moscow, 2001) [in Russian].
B. E. Pobedrya, Numerical Methods in Elasticity and Plasticity Theory (Izd-vo MGU, Moscow, 1995) [in Russian].
D. V. Georgievskii, “Compression and outflow of an asymptotically thin perfectly rigid-plastic spherical layer,” Moscow Univ. Mech. Bull. 66 (6), 148–150 (2011).
V. F. Kravchenko, G. A. Nesenenko, and V. I. Pustovoit, Poincaré Asymptotics of Solution to Problems of Irregular Heat and Mass Transfer (Fizmatlit, Moscow, 2006) [in Russian].
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated by A. A. Borimova
About this article
Cite this article
Shabaikin, R.R. Dynamic Deformation Effects During Compression and Drain of Asymptotically Thin Perfectly Rigid Plastic Spherical Layer. Mech. Solids 55, 172–176 (2020). https://doi.org/10.3103/S0025654420020168
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.3103/S0025654420020168