Developing a hybrid computational model of AFM indentation for analysis of mechanically heterogeneous samples

Standard analysis methods for atomic force microscope (AFM) indentation experiments use Hertzian contact mechanics to extract local elastic properties assuming a homogeneous sample material. In contrast, most biological materials have heterogeneous structure and composition. We previously introduced a non-Hertzian analysis method to detect depth-dependent elastic properties from indentation depth, force and geometry information. In this study we employ a modified Eshelby model to characterize the elastic properties of heterogeneous substrates with discrete embedded inclusions. In this hybrid computational model, we estimate the contribution of inclusions with known size and moduli to the overall indentation response of a heterogeneous substrate based on the effective volume fraction of constituents within the indentation field. For wide ranges of indenter size and inclusion geometry, simulations reveal a consistent ellipsoidal indentation field, suggesting the Eshelby model may be applicable for large discrete inclusions. This novel technique provides a potential means to calculate inclusion properties of heterogeneous materials, such as cells and tissues, using AFM indentation without physical deconstruction of the composite sample.