Vol. 6, No. 1-4, 2011

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Conical indentation of thick elastic spherical shells

Nkem Ogbonna and Alan Needleman

Vol. 6 (2011), No. 1-4, 443–451

Indentation of spherical shells by a rigid conical indenter is analyzed. Because the shape change associated with overall bending provides a main deviation from the corresponding indentation behavior of a half-space, finite deformation analyses are carried out. The shell material is characterized by a hypoelastic relation that reduces to isotropic linear elasticity for small strains and is an elastic relation at finite strains for fixed principal directions. Axisymmetric deformations are assumed. For indentation of shells there is a complex interaction between the indentation response and the overall structural response of the shell. The aim of the analyses is to give insight into the range of indentation depths for which the indentation response dominates so that an indentation analysis can be used to extract the elastic properties. Shells having various thicknesses are analyzed. It is found that for spherical shells with thickness to radius ratios less than or equal to 0.4 and for sufficiently shallow indentation depths, the scaling of the indentation load with contact area has the same form as that for indentation into a half-space but with a different scaling constant.

indentation, elasticity, spherical shells, finite element modeling
Received: 24 April 2010
Revised: 18 August 2010
Accepted: 18 August 2010
Published: 28 June 2011
Nkem Ogbonna
Department of Mathematics, Statistics and Computer Science
Michael Okpara University of Agriculture
Umudike, Abia State
Alan Needleman
Department of Materials Science and Engineering
College of Engineering and Center for Advanced Scientific Computing and Modeling (CASCaM)
University of North Texas
1155 Union Circle #305310
Denton, TX 76203-50175
United States