×

Void formation and growth in a class of compressible solids. (English) Zbl 0891.73013

Summary: A new class of compressible elastic solids, which includes the Blatz-Ko material as a special case, is proposed. A closed-form solution is constructed and studied for a bifurcation problem modeling void formation in this class. The relation between the void-formation condition and the material parameters is obtained analytically. An energy comparison of the void-formation deformation and the homogeneous expansion deformation is carried out.

MSC:

74B20 Nonlinear elasticity
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] C.C. Chu and A. Needleman, Void nucleation effects in biaxially stretched sheets, J. Engrg. Mat. Tech. 102 (1980) 249-256
[2] S.H. Goods and L.M. Brown, The nucleation of cavities by plastic deformation, Acta Met. 27 (1979) 1-15.
[3] A.L. Gurson, Continuum theory of ductile rupture by void nucleation and growth: part I ?yield criteria and flow rules for porous ductile media, J. Engrg. Mat. Tech. 99 (1977) 1-15.
[4] A. Needleman, Void growth in an elastic-plastic medium, J. Appl. Mech. 39 (1972) 964-970.
[5] V. Tvergaard, Ductile fracture by cavity nucleation between larger voids, J. Mech. Phys. Solids. 30 (1982) 256-286. · Zbl 0491.73118
[6] V. Tvergaard, Influence of void nucleation on ductile shear fracture at a free surface, J. Mech. Phys. Solids. 30 (1982) 399-425. · Zbl 0496.73087
[7] V. Tvergaard, Material failure by void growth to coalescence, Adv. Appl. Mech. 27 (1990) 83-151. · Zbl 0728.73058
[8] A.N. Gent and P.B. Lindley, Internal rupture of bonded rubber cylinders in tension. Proc, R. Soc. Lond.A249 (1958) 195-205.
[9] J.M. Ball, Discontinuous equilibrium solutions and cavitation in nonlinear elasticity, Phil. Trans. Roy. Soc. LondonA306 (1982) 557-611. · Zbl 0513.73020
[10] R. Abeyaratne and C.O. Horgan, Initiation of localized plane deformations at a circular cavity in an infinite compressible nonlinearly elastic medium. J. Elasticity 15 (1985) 243-256. · Zbl 0574.73050
[11] S.S. Antman and P.V. Negron-Marrero, The remarkable nature of radially symmetric equilibrium states of aelotropic nonlinearly elastic bodies, J. Elasticity 18 (1987) 131-164. · Zbl 0631.73016
[12] D.-T. Chung, C.O. Horgan and R. Abeyaratne, The finite deformation of internally pressurized hollow cylinders and spheres for a class of compressible elastic materials, Int. J. Solids Structures 22 (1986) 1557-1570. · Zbl 0603.73038
[13] M. Giaqunta, G. Modica and J. Soucek, Cartesian currents, weak diffeomorphisms and existence theorems in nonlinear elasticity, Arch. Rational Mech. Anal. 106 (1989) 97-159. · Zbl 0677.73014
[14] C.O. Horgan and R. Abeyaratne, A bifurcation problem for a compressible nonlinear elastic medium: growth of a micro-void, J. Elasticity 16 (1986) 189-200. · Zbl 0585.73017
[15] C.O. Horgan and T. Pence, Void nucleation in tensile dead-loading of a composite incompressible nonlinear elastic sphere, J. Elasticity 21 (1989) 61-82. · Zbl 0687.73017
[16] C.O. Horgan and T. Pence, Cavity formation at the center of a composite incompressible nonlinear elastic sphere, Trans. ASME. 56 (1989) 302-308. · Zbl 0711.73042
[17] R.D. James and S.J. Spector, The formation of filamentary voids in solids, IMA Preprint Series 572, University.
[18] K.A. Pericak-Spector and S.J. Spector, Nonuniqueness for a hyperbolic system: cavitation in nonlinear elastodynamics, Arch. Rational Mech. Anal. 101 (1988) 293-317. · Zbl 0651.73005
[19] P. Podio-Guidugli, G. Vergara Caffarelli and E.G. Virga, Discontinuous energy minimizers in nonlinear elastostatics: an example of J. Ball revisited, J. Elasticity 16 (1986) 75-96. · Zbl 0575.73021
[20] J. Sivaloganathan, Uniqueness of regular and singular equilibria for spherically symmetric problems of nonlinear elasticity. Arch. Rational Mech. Anal. 96 (1986) 589-604. · Zbl 0628.73018
[21] J. Sivaloganathan, A field theory approach to stability of equilibria in radial elasticity, Math. Proc. Camb. Phil. Soc. 99 (1986) 589-604. · Zbl 0612.73013
[22] C.A. Stuart, Radially symmetric cavitation for hyperelastic materials, Ann. Inst. Henri Poincare: Nonlinear Anal. 2 (1985) 33-66. · Zbl 0588.73021
[23] P.J. Blatz and W.L. Ko, Application of finite elastic theory to the deformation of rubbery materials, Trans. Soc. Rheology 6 (1962) 223-251.
[24] G.W. Bluman and S. Kumei, Symmetries and Differential Equations, Springer-Verlag, New York (1989) 412 pp. · Zbl 0698.35001
[25] C.Von Westenholz, Differential Forms in Mathematical Physics, North-Holland, New York (1981) 563 pp. · Zbl 0391.58001
[26] D.M. Haughton, On non-existence of cavitation in incompressible elastic membranes, Q. J. Mech. Appl. Math. 39 (1986) 289-296. · Zbl 0582.73022
[27] D.M. Haughton, Cavitation in compressible elastic membranes, Int. J. Engrg. Sci. 28 (1990) 163-168.
[28] R.W. Ogden, Nonlinear Elastic Deformations, Ellis Horwood, Chichester, West Sussex, England (1984) 532 pp. · Zbl 0541.73044
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.