Uniqueness of Elastoplastic Properties Measured by Instrumented Indentation

  • L. LiuEmail author
  • Xi ChenEmail author
  • N. OgasawaraEmail author
  • N. Chiba
Reference work entry


Indentation is widely used to extract material elastoplastic properties from the measured load-displacement curves. One of the most well-established indentation technique utilizes dual (or plural) sharp indenters (which have different apex angles) to deduce key parameters such as the elastic modulus, yield stress, and work-hardening exponent for materials that obey the power-law constitutive relationship. Here we show the existence of “mystical materials,” which have distinct elastoplastic properties, yet they yield almost identical indentation behaviors, even when the indenter angle is varied in a large range. These mystical materials are, therefore, indistinguishable by many existing indentation analyses unless extreme (and often impractical) indenter angles are used. Explicit procedures of deriving these mystical materials are established, and the general characteristics of the mystical materials are discussed. In many cases, for a given indenter angle range, a material would have infinite numbers of mystical siblings, and the existence maps of the mystical materials are also obtained. Furthermore, we propose two alternative techniques to effectively distinguish these mystical materials. In addition, a critical strain is identified as the upper bound of the detectable range of indentation, and moderate tailoring of the constitutive behavior beyond this range cannot be effectively detected by the reverse analysis of the load-displacement curve. The topics in this chapter address the important question of the uniqueness of indentation test, as well as providing useful guidelines to properly use the indentation technique to measure material elastoplastic properties.


Indentation Elastoplastic properties Unique solution Numerical study Indistinguishable load-displacement curve Reverse analysis Detectable strain range Critical strain Loading curvature Indenter angle 



The work is supported in part by National Science Foundation CMS-0407743 and CMMI-CAREER-0643726 and in part by the Department of Civil Engineering and Engineering Mechanics, Columbia University.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mechanical and Aerospace EngineeringUtah State UniversityLoganUSA
  2. 2.Department of Earth and Environmental EngineeringColumbia Nanomechanics Research Center, Columbia UniversityNew YorkUSA
  3. 3.Department of Mechanical EngineeringNational Defense Academy of JapanYokosukaJapan
  4. 4.National Defense Academy of JapanYokosukaJapan

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