Mechanical response of homogeneous elastic materials to AFM indentation with conical tips with finite apex curvature

Finite element analysis (FEA) and the method of dimensionality reduction (MDR) are employed to investigate non-adhesive, linear elastic indentation of half-space materials by rigid atomic force microscopy (AFM) tips. Two realistic AFM tip geometries are considered: a cone with a parabolic apex (intact tip) and a truncated cone (damaged tip). FEA results align well with MDR analytical solutions for axisymmetric contact. Unlike the idealized conical model with zero apex radius, indentation force–depth curves for realistic tips are best described by a second-order polynomial with a linear term dependent on either the tip radius of curvature (intact conical tips) or the base radius (truncated conical tips). Experimental AFM indentations on polydimethylsiloxane conducted with an initially sharp AFM tip and then with progressively worn tips of the same AFM probe confirm these findings. Applying Sneddon’s indentation model without accounting for finite apex curvature of the AFM tips significantly overestimates the material’s Young’s modulus. FEA further shows that substrate effects intensify with increasing tip curvature when thin materials are indented on rigid substrates.