Study of possible void nucleation and growth in solids in the framework of the Davis-Nadai deformation theory

A. A. Il’yushin, Plasticity, Part 1: Elastoplastic Deformations (OGIZ, Moscow-Leningrad, 1948) [in Russian].

V. I. Betekhtin, S. Yu. Veselkov, Yu. M. Dal’, et al., “Theoretical and Experimental Investigation of the Effect of an Applied Load on Pores in Solids,” Fiz. Tverd. Tela 45(4), 618–624 (2003) [Phys. Solid State (Engl. Transl.) 45 (4), 649–655 (2003)].

A. S. Grigoriev, On the Theory and Problems of Shell Equilibrium under Large Deformations,” Izv. Akad. Nauk SSSR.Mekh. Tverd. Tela, No. 1, 163–168 (1970) [Mech. Solids (Engl. Transl.)].

E. P. Kolpak, Stability of Membrane Shells under Large Strains (Izd-vo SPbGU, St. Petersburg, 2000) [in Russian].

S. A. Kabrits, E. I. Mukhailovskii, P. E. Tovstik, et al., General Nonlinear Theory of Elastic Shells (Izd-vo SPbGU, St. Petersburg, 2002) [in Russian].

A. I. Lurie, Nonlinear Theory of Elasticity (Nauka, Moscow, 1980) [in Russian].

J. M. Ball, “Discontinuous Equilibrium Solutions and Cavitation in Nonlinear Elasticity,” Phil. Trans. Roy. Soc. London. Ser. A:Math. Phys. Sci. 306(1496), 557–611 (1982).

S. A. Stuart, “Radially Symmetric Cavitation for Hyperelastic Materials,” Ann. Inst. Henry Poincare — Anal. Nonlin. 2, 33–66 (1985).

C. O. Horgan and R. Abeyaratne, “A Bifurcation Problem for Compressible Nonlinearly Elastic Medium: Growth of a Micro-Void,” J. Elasticity 16, 189–200 (1986).

J. Sivaloganathan, “Uniqueness of Regular and Singular Equilibria for Spherically Symmetric Problems of Nonlinear Elasticity,” Arch. Rat. Mech. Anal. 96(2), 97–136 (1986).

M.-S. Chou-Wang and C. O. Horgan, “Void Nucleation and Growth for a Class of Incompressible Nonlinearly Elastic Materials,” Int. J. Solids Struct. 25, 1239–1254 (1989).

T. Hao, “A Theory of the Appearance and Growth of the Micro-Spherical Void,” Int. J. Fract. 43, 51–55 (1990).

F. Meynard, “Existence and Non-Existence Results on the Radially Symmetric Cavitation Problem,” Quart. Appl.Math. 50, 210–226 (1992).

C. O. Horgan, “Void Nucleation and Growth for CompressibleNon-Linearly Elastic Material: An Example,” Int. J. Solids Struct. 29(3), 279–291 (1992).

H.-S. Hou and R. Abeyaratne, “Cavitation in Elastic and Elastic-Plastic Solids,” J. Mech. Phys. Solids 40(3), 571–592 (1992).

X.-C. Shang and C.-J. Cheng, “Exact Solutions for Cavitated Bifurcation for Compressible Hyperelastic Materials,” Int. J. Engng Sci. 39, 1101–1117 (2001).

J. Diani, “Irreversible Growth of a Spherical Cavity in Rubber-Like Material: A Fracture Mechanics Description,” Int. J. Fract. 112, 151–161 (2001).

J.-S. Ren and C.-J. Cheng, “Bifurcation of Cavitation Solutions for Incompressible Transversely Isotropic Hyperelastic Materials,” J. Engng Math. 44, 245–257 (2002).

I. A. Brigadnov, “The Dual Approach to the Evaluation of the Load-Carrying Capacity of Nonlinearly Elastic Bodies,” Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 2, 39–46 (2004) [Mech. Solids (Engl. Transl.) 39 (2), 30–35 (2004)].

E. Davis, “Stress Growth with Strain Variation and “Stress-Strain” Dependence in Plastic Region for Copper in Complex Stress State,” in Theory of Plasticity, Ed. by Yu. N. Rabotnov (Izd-vo Inostr. Liter., Moscow, 1948) [in Russian].

A. Nadai, Theory of Flow and Fracture of Solids, Vol. 1 (NewYork-Toronto-London, 1950; Izd-vo Inostr. Liter., Moscow, 1954).

R. Hill, The Mathematical Theory of Plasticity (Clarendon, Oxford, 1950; Gostekhizdat, Moscow, 1956).

R. F. Bishop, R. Hill, and N. F. Mott, “The Theory of Indentation and Hardness Tests,” Proc. Phys. Soc. 57, 147–159 (1945).

F. A. McClintock, “A Criterion for a Ductile Fracture by the Growth of Holes,” J. Appl. Mech. (Trans. ASME. Ser. E) 35(2), 363–371 (1968).

J. R. Rice and D.M. Tracey, “On the Ductile Enlargement of Voids in Triaxial Stress Fields,” J.Mech. Phys. Solids 17(3), 201–217 (1969).

Y. Huang, J. W. Hutchinson, and V. Tvergaard, “Cavitation Instabilities in Elastic-Plastic Solids,” J. Mech. Phys. Solids 39, 223–242 (1991).

V. Tvergaard, Y. Huang, and J.W. Hutchinson, “Cavitation Instabilities in a Power Hardening Elastic-Plastic Solids,” Europ. J.Mech. Ser. A: Solids 11(2), 215–231 (1992).

Yu.M. Dal’ and Yu. G. Pronina, “Deformation of Spherical Pore in Nonlinear-Elastic Solid,” Izv. Ross. Akad. Nauk. Ser. Fiz. 70(9), 1341–1343 (2006) [Bull. Russ. Acad. Sci. Phys. (Engl. Transl.) 70 (9), 1533–1535 (2006)].

Yu. M. Dal’ and Yu. G. Pronina, “Void Growth and Healing in Elastic-Plastic Body under the Action of Hydrostatic Pressure,” Electronic Journal “Investigated in Russia” 9, 1387–1394 (2006). URL: http://zhurnal.ape.relarn.ru/articles/2006/148.pdf .

A. A. Morshchinina, “Nonlinear Axisymmetric Elasticity Problem for a Hollow Sphere,” Vestnik S.-Peterburg. Univ. Mat. Mekh. Astr., No. 4, 84–88 (2009).

V. I. Betekhtin, A. M. Glezer, A. G. Kadomtsev, et al., “Excess Free Volume and Mechanical Properties of Amorphous Alloys,” Fiz. Tverd. Tela 40(1), 85–89 (1998) [Sov. Phys. Solid State (Engl. Transl.) 40 (1), 74–78 (1998)].

V. I. Smirnov, Course of Higher Mathematics (Gostekhizdat, Moscow-Leningrad, 1951) [in Russian].

A. A. Il’yushin, Plasticity. Foundations of General Mathematical Theory (Izd-vo AN SSSR, Moscow, 1963) [in Russian].

A. N. Gent and P. B. Lindey, “Internal Rupture of Bounded Rubber Cylinders in Tension,” Proc. Roy. Soc. London. Ser. A 249, 195–205 (1958).

A. A. Gruzdkov, N. F. Morozov, and Yu. V. Petrov, “Equal Power Principle in Multilevel Dynamic Fracture of Solids,” Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 6, 167–172 (2006) [Mech. Solids (Engl. Transl.) 41 (6), 135–139 (2006)].