Dynamic deformation of an elastoviscoplastic hollow sphere. (English. Russian original) Zbl 1272.74078
J. Appl. Mech. Tech. Phys. 50, No. 5, 872-877 (2009); translation from Prikl. Mekh. Tekh. Fiz. 50, No. 5, 169-175 (2009).
Summary: The stress-strain state of a hollow sphere under time-dependent loading is studied using the constitutive relations for a hardening compressible elastoviscoplastic sold. Analytical solutions are obtained for displacement fields in the elastic and plastic regions. Time dependences of the reciprocal of the radius of the elastoplastic boundary are constructed, and the effect of the physicomechanical parameters on the radius of the elastoplastic boundary is determined.
MSC:
| 74C10 | Small-strain, rate-dependent theories of plasticity (including theories of viscoplasticity) |
References:
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| [2] | A. N. Sporykhin, Perturbation Method in Stability Problems for Complex Media [in Russian], Voronezh State Univ., Voronezh (1997). |
| [3] | T. D. Semykina, ”Triaxial extension of elastoplastic space with a spherical cavity,” Izv. Akad. Nauk SSSR, Mekh. Mashinostr., No. 1, 17–21 (1963). |
| [4] | A. N. Sporykhin and A. I. Shashkin, Stability of Equilibrium of Bulk Solids and Problems of Rock Mechanics [in Russian], Fizmatlit, Moscow (2004). |
| [5] | D. D. Ivlev and A. Yu. Ishlinskii, Mathematical Theory of Plasticity [in Russian], Fizmatlit, Moscow (2001). |
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