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Numerical Analysis of Indentation of an Elastic Hemispherical Shell

Published online by Cambridge University Press:  15 July 2015

Y.-F. Jia ,
F.-Z. Xuan  and
F.-Q. Yang
Y.-F. Jia
Affiliation:
Key Laboratory of Pressure System and Safety (MOE)School of Mechanical and Power EngineeringEast China University of Science and TechnologyShanghai, P.R. China
F.-Z. Xuan
Affiliation:
Key Laboratory of Pressure System and Safety (MOE)School of Mechanical and Power EngineeringEast China University of Science and TechnologyShanghai, P.R. China
F.-Q. Yang*
Affiliation:
Materials ProgramDepartment of Chemical and Materials EngineeringUniversity of Kentucky Lexington, USA
*
*Corresponding author (fyang2@uky.edu)
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Abstract

Nanoindentation technique has been used to measure the elastic modulus of virus capsids, capsules, vesicles, and tubules. The principle of the nanoindentation technique is based on the elastic solution of an isotropic, homogeneous, semi-infinite material, which limits the use of nanoindentation in measuring the mechanical properties of materials of small scales. To address this limitation, Reissner's thin shell model, which is based on the point indentation on a thin shell, has been used in analyzing the indentation of thin shells. In this work, the indentation of elastic hemispherical shells of various thicknesses by a rigid, spherical indenter is analyzed, using the finite element method. The simulation results reveal the limitation of the Reissner's thin shell model. A semi-analytical relationship between the indentation depth and the indentation load is proposed, which consists of the contributions of the Hertz's local deformation, the Reissner's local flattening, and the Pogorelov's deflection of the shell. This relationship provides an analytical basis of using nanoindentation to determine the nominal contact modulus of spherical shells. The comparison between the numerical results and the experimental results in literature supports the proposed semi-analytical relationship and reveals the effect of viscoelastic characteristic of shell structures on the indentation deformation.

Keywords

Indentation (normal, micro and nano)Elastic propertiesBiomaterialsFinite element analysis
Type
Research Article
Information
Journal of Mechanics , Volume 32 , Issue 3 , June 2016 , pp. 245 - 253
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2016 

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