The purpose of this work is to probe the analytical formulation of the mechanical response [Formula: see text], which is the consequence of determining the connection between charge and depth values. It is possible to acquire the [Formula: see text] expression by doing an indentation experiment while the loading process is unfolding. In this particular piece of research, the formulation of [Formula: see text] takes into consideration the pile-up mode for an indenter with a spherical structure. The remarkable concordance that exists involving the newly propositioned appearance and the outcome of the experiments has been presented in this academic work. An experimental investigation is being conducted on ductile materials, namely copper and the alloys of copper.