Nonlinear analysis of oscillatory indentation in elastic and viscoelastic solids

Yang Tse Cheng, Wangyang Ni, Che Min Cheng

Research output: Contribution to journalArticlepeer-review

54 Scopus citations


Determining the mechanical properties at micro- and nanometer length scales using nanoindentation or atomic force microscopy is important to many areas of science and engineering. Here we establish equations for obtaining storage and loss modulus from oscillatory indentations by performing a nonlinear analysis of conical and spherical indentation in elastic and viscoelastic solids. We show that, when the conical indenter is driven by a sinusoidal force, the square of displacement is a sinusoidal function of time, not the displacement itself, which is commonly assumed. Similar conclusions hold for spherical indentations. Well-known difficulties associated with measuring contact area and correcting thermal drift may be circumvented using the newly derived equations. These results may help improve methods of using oscillatory indentation for determining elastic and viscoelastic properties of solids.

Original languageEnglish
Article number075506
JournalPhysical Review Letters
Issue number7
StatePublished - 2006

Bibliographical note

Publisher Copyright:
© 2006 The American Physical Society.

ASJC Scopus subject areas

  • General Physics and Astronomy


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