Indentation is widely used to measure material mechanical properties such as hardness, elastic modulus, and fracture toughness (for brittle materials). Can one use indentation to extract material elastoplastic properties directly from the measured force-displacement curves? Or simply, is it possible to obtain material stress-strain curves from the corresponding indentation load-displacement curves? In an upcoming paper in JMPS titled "On the uniqueness of measuring elastoplastic properties from indentation: The indistinguishable mystical materials," Xi Chen and colleagues at Columbia University and National Defense Academy, Japan 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. The authors have established explicit procedures of deriving these mystical materials. 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, they propose two alternative techniques to effectively distinguish these mystical materials. The study in this paper addresses 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.

As an indenter penetrates an elastoplastic material, the indentation load P can be measured as a continuous function of the indentation displacement δ, to obtain the so-called P-δ curve. A primary goal of the indentation analysis is to relate the material elastoplastic properties (such as the Young's modulus, yield stress, and work-hardening exponent) with the indentation response (i.e. the shape factors of the P-δ curve, including its curvature, unloading stiffness, loading work, unloading work, maximum penetration, residual penetration, maximum load, etc.). The sharp indenters (e.g. Berkovich or Vickers) are the most widely used in practice.