Orientation effect on the Boussinesq indentation of a transversely isotropic piezoelectric material

Ming Liu, Fuqian Yang

Research output: Contribution to journalArticlepeer-review

29 Scopus citations


Three-dimensional finite element analysis was used to study the effect of the angle between the loading direction and the axisymmetric direction on the indentation behavior of a transversely isotropic piezoelectric half-space by a cylindrical indenter of flat end. Two cases were considered in the analysis, which included (a) the indentation by an insulating indenter, and (b) the indentation by a conducting indenter. Both the indentation load and the indentation-induced potential were found to be proportional to the indentation depth. Using the simulation results and the analytical relationship for the indentation by a rigid, insulating indenter, semi-analytical relationships were developed between the indentation load and the indentation depth and between the indentation-induced potential on the indenter and the indentation depth for the conducting indenter, respectively. The proportionality between the indentation-induced potential and the indentation depth is only a function of the angle between the loading direction and the poling direction, independent of the type of indenters, which may be used to measure the relative direction of the loading axis to the axisymmetric axis of transversely piezoelectric materials from the indentation test.

Original languageEnglish
Pages (from-to)2542-2547
Number of pages6
JournalInternational Journal of Solids and Structures
Issue number14-15
StatePublished - Jul 2013

Bibliographical note

Funding Information:
This work is supported by the NSF through Grant No CMMI-0800018 . The authors would like to thank the University of Kentucky Information Technology Department and Center for Computational Sciences for computing time on the Lipscomb High Performance Computing Cluster. This research was supported in part by the NSF through XSEDE resources provided by SDSC (National allocation).


  • 3-D FEM simulation
  • Indentation deformation
  • Load-displacement relation
  • Piezoelectric materials

ASJC Scopus subject areas

  • Modeling and Simulation
  • General Materials Science
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics


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