A dataset for calculating Young's modulus in deep spherical indentations

Atomic Force Microscopy (AFM) is a powerful tool for determining the mechanical properties of soft materials at the nanoscale. When using spherical indenters, the data is usually fitted to the classic Hertzian equation which is valid for parabolic indenters, or spherical indenters for small indentation depths compared to the tip radius (i.e. h/R«1). However, for bigger indentation depths, more complex equations should be used for data fitting. In this paper, a straightforward energy-based approach is proposed to determine the Young's modulus of soft samples without the need for a fitting procedure. By calculating the integral of the function that relates the force to the indentation depth for deep spherical indentations, an equation was derived that relates the work done by the indenter (W) to the h/R ratio. The Young's modulus (E) can be easily determined by calculating the work done by the indenter (which is equal to the area under the force-indentation data) and using a function that depends on the h/R ratio (i.e., X = f (h/R)). In this dataset article, the function X = f (h/R) and a table including the X-values corresponding to different h/R values in the domain 0 ≤ h/R ≤ 5 are presented. An example demonstrating indentation experiments on an agarose gel is also included. This proposed approach represents the simplest way to generate Young's modulus maps, as it only requires calculating the area under the force-indentation data and using the X-values presented in this dataset article.