Experimental Mechanics

, Volume 53, Issue 5, pp 731–742 | Cite as

Nonlinearly Viscoelastic Nanoindentation of PMMA Under a Spherical Tip

  • Y. KucukEmail author
  • C. Mollamahmutoglu
  • Y. Wang
  • H. Lu


The Oliver-Pharr method has been well established to measure Young’s modulus and hardness of materials without time-dependent behavior in nanoindentation. The method, however, is not appropriate for measuring the viscoelastic properties of materials with pronounced viscoelastic effects. One well-known phenomenon is the formation of unloading “nose” or negative stiffness during unloading that often occurs during slow loading-unloading in nanoindentation on a viscoelastic material. Most methods in literature have only considered the loading curve for analysis of viscoelastic nanoindentation data while the unloading portion is not analyzed adequately to determine the nonlinearly viscoelastic properties. In this paper, nonlinearly viscoelastic effects are considered and modeled using the nonlinear Burgers model. Nanoindentation was conducted on poly-methylmethacrylate (PMMA) using a spherical indenter tip. An inverse problem solving approach is used to allow the finite element simulation results to agree with the nanoindentation load–displacement curve during the entire loading and unloading stage. This approach has allowed the determination of the nonlinearly viscoelastic behavior of PMMA at submicron scale. In addition, the nanoindentation unloading “nose” has been captured by simulation, indicating that the negative stiffness in the viscoelastic material is the result of memory effect in time-dependent materials.


Nanoindentation Nonlinear viscoelastic Nonlinear Burgers model Polymer PMMA Finite element method 



We acknowledge the support of NSF under grant CMMI-1132174 with Dr. Clark Cooper as the program director.


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Copyright information

© Society for Experimental Mechanics 2012

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringBartin UniversityBartinTurkey
  2. 2.Department of Mechanical EngineeringThe University of Texas at DallasRichardsonUSA
  3. 3.Intel CorporationChandlerUSA

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