Effects of surface energy and substrate on modulus determination of biological films by conical indentation

Micro-/nano-indentation has become prevalent in evaluating the mechanical characteristics of biological samples, such as cells and tissues. However, the existing contact models describing conical indentation ignore the joint effects of surface energy and substrate, and consequently cannot accurately extract the Young’s modulus of biological samples deposited on substrate. Through finite element methods, we examine the conical indentation of biological films on substrates while taking surface energy into account. Based on the dimensional analysis, the explicit relationship between load and indentation depth is achieved for films with their moduli varying from 0.001 to 100 times that of the substrate. If the classical Sneddon’s model was employed to analyze the load-depth data, the measured modulus could reach 18 times the real modulus for films on harder substrates, but only 4% of the real modulus for films on softer substrates. Meanwhile, in micro-/nano-indentations, neglecting the contribution of surface energy would result in an overestimation of the Young’s modulus of films depending on the contact size. The analytical expression provided here can be utilized to precisely deduce the mechanical characteristics of biological films deposited on substrate from the load and indentation depth data of a conical indentation. © Science China Press 2024.