In the present study, a semi-empirical modeling of the mechanical response in pile-up mode is obtained by deriving the load-depth relationship during the indentation loading cycle. The advantage compared to the relations previously used is that this new expression is a function of the predictable criterion of the mode of deformation, (hf/hm), which makes it possible to distinguish the sink-in mode from the pile-up mode. A comparison between the proposed expression and the results of the instrumented indentation tests shows excellent agreement.
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