Equilibrium State of a Softening Elastoplastic Medium with an Expanding Spherical Cavity
This paper describes the problem of a stress–strain state arising from expansion of a spherical cavity under increasing internal pressure. The properties of a medium are described by a single curve with a descending section (Hencky medium with softening) under the condition of nonpositivity of volume deformation. An iteration procedure for calculation of equilibrium parameters is proposed. This procedure is based on the method of simple iterations. Numerical calculations confirming the developed technique are presented.
KeywordsHencky medium polar-symmetric deformation softening method of simple iterations convergence stability
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- 3.N. G. Chausov, “Total Deformation Diagrams As a Source of Information about the Kinetics of Damage Accumulation and Resistance to Fracture of Materials,” Zavod. Lab. Diagn. Mater. 70 (7), 42–49 (2004).Google Scholar
- 6.V. E. Vil’deman and M. P. Tret’akov, “Testing ofMaterials to the Construction of Total Deformation Diagrams,” Probl. Mashinostr. Nadezh. Mashin, No. 2, 93–98 (2013).Google Scholar
- 7.V. V. Struzhanov and E. A. Bakhareva, “Mathematical Methods in the Theory of Pure Bending of Rectangular Beams of Softening Material with a Symmetric Stress–Strain Diagram,” Vychisl. Mekh. Splosh. Sred 5 (2), 158–167 (2012).Google Scholar
- 8.V. V. Struzhanov and V. I. Mironov, Strain Softening of Materials in Structural Elements (Izd. Ural. Otd. Ross. Akad. Nauk, Ekaterinburg, 1995) [in Russian].Google Scholar
- 13.K. V. Berdnikov and V. V. Struzhanov, “Residual Stresses in an Elastoplastic Space, Arising after the Expansion of a Spherical Cavity,” Vestn. Ural. Gos. Univ. Putei Soobshch., No. 2, 18–26 (2013).Google Scholar
- 14.A. A. Samarskii and A. V. Gulin, Numerical Methods (Nauka, Moscow, 1989) [in Russian].Google Scholar
- 15.I. S. Berezin, N. P. Zhidkov, and G. M. Kobel’kov, Numerical Methods (Izd. Binom. Lab. Znanii, 2003) [in Russian].Google Scholar
- 16.A. A. Baryakh, V. A. Asanov, and I. L. Pan’kov, Physical and Mechanical Properties of Salt Rocks of the Verkhnekamskoye Potassium Deposit (Perm. Gos. Tekh. Univ., Perm, 2008) [in Russian].Google Scholar