Abstract
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.
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References
V. P. Radchenko, E. V. Nebogina, and M. V. Basov, “Structural Model of Supercritical Elastic–Plastic Deformation of Materials under Uniaxial Tensile,” Vestn. Sam. Gos. Tekh. Univ., Fiz.-Mat. Nauki, No. 9, 55–65 (2000).
Z. P. Bažant and L. Cedolin, Stability of Structures: Elastic, Inelastic, Fracture and Damage Theories (Oxford Univ. Press, New York, 2003).
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).
K. Y. Volokh, “Softening Hyperelasticity for Modeling Material Failure: Analysis of Cavitation in Hydrostatic Tension,” Int. J. Solids Structures, No. 44, 5043–5055 (2007).
Yu. I. Kadashevich and S. P. Pomytkin, “Formulation of the Criterion for the Strength of Materials for Endochronic Theory of Inelasticity with Account for Microfractures in Large Deformations,” Vestn. Sam. Gos. Tekh. Univ., Ser. Fiz.-Mat. Nauki, No. 1, 53–59 (2010).
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).
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).
V. V. Struzhanov and V. I. Mironov, Strain Softening of Materials in Structural Elements (Izd. Ural. Otd. Ross. Akad. Nauk, Ekaterinburg, 1995) [in Russian].
V. V. Struzhanov and K. V. Berdnikov, “Constitutive Relationships of the Hencky Medium for Softening Materials in a Diagonal Strain Tensor,” Vestn. Sam. Gos. Univ., Ser. Fiz.-Mat. Nauki, No. 3, 72–80 (2012).
A. I. Lurie, Theory of Elasticity (Springer-Verlag Berlin Heidelberg, The Netherlands, 2005).
A. A. Il’yushin, Plasticity, Vol. 1: Elastoplastic Deformations (Logos, Moscow, 2004) [in Russian].
S. P. Timoshenko and J. N. Goodier, Theory of Elasticity (Nauka, Moscow, 1975; McGraw-Hill, 1970).
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).
A. A. Samarskii and A. V. Gulin, Numerical Methods (Nauka, Moscow, 1989) [in Russian].
I. S. Berezin, N. P. Zhidkov, and G. M. Kobel’kov, Numerical Methods (Izd. Binom. Lab. Znanii, 2003) [in Russian].
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].
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Original Russian Text © K.V. Berdnikov, V.V. Struzhanov.
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 59, No. 1, pp. 120–128, January–February, 2018.
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Berdnikov, K.V., Struzhanov, V.V. Equilibrium State of a Softening Elastoplastic Medium with an Expanding Spherical Cavity. J Appl Mech Tech Phy 59, 104–111 (2018). https://doi.org/10.1134/S0021894418010133
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DOI: https://doi.org/10.1134/S0021894418010133