Expansion OF A Spherical Cavity At The Center Of A Non-Homogeneous Sphere Of Ductile Metal Under Internal And External Pressures


L.K. Roy,




non-homogeneous sphere, ,ductile metal, ,internal and external pressure, spherical cavity, ,


The aim of this paper is to investigate the distribution of stresses due to expansion of a spherical cavity at the center of a non-homogeneous metallic sphere of finite radius for an elasto-plastic solid under an increasing internal pressure, the external pressure remaining constant. The non-homogeneity of the elastic material is characterised by supposing that the lame constrants very exponentially as the function of radial distance. The case of ideal plastic solid has been deducted from this general case.


I.  R. Hill (1950) : Theory of Plasticity, Oxford University Press, p-317

II.  A.E.H. Love(1952) : The Mathematical Theory of Elasticity, Dover Publication, p-164, London.

III.  Saint-Venant(1865) : Jour. De-Math, Primes at appl.(lonvilla) t-10.

IV.  S.G. Lekhnitskii (1963) : Theory of elasticity of an Anisotropic Elastic Body, Holden-Dey, Inc, p-390.

V.  H.C.Hopkins (1960) : Progress in solid Mechanics, Vol.1, p-80, Edited by I.N.Eneddon and R.Hill, North Holland Publishing Company, Amsterdem.

VI.  P.R.Sengupta (1969) : Ind.Jour. Mech and Math., Special issue, aprt-II, p-80, prof. B.sen, D.Se., F.N.I., 70th Birth Anniversary volume.

VII.  L.K. Roy (1992) :  Proc. Nat. Acad. Sci. India, 62(A), III p-445.

L.K Roy View Download