A multi-sphere indentation method to determine Young's modulus of soft polymeric materials based on the Johnson?Kendall?Roberts contact model

Tissue cells can sense mechanical properties of their surroundings, which, in vitro, generally refer to substrates coated with proteins. The elastic moduli of soft polymers used as substrates have been proved to affect many cellular processes, such as migration, development, and even differentiation. In this note, we present a cost-effective experimental design by using multi-sphere indentations to find the relation between indentation depth and sphere radius, and then apply the Johnson–Kendall–Roberts (JKR) contact theory with consideration of adhesive work to fit the experimental results so as to assess the value of Young's modulus. Two compliant polymeric materials, polyacrylamide gels and polydimethylsiloxane elastomers, are tested with this method. The results are in good agreement with those reported by previous experiments. Comparisons between JKR and traditional Hertz fittings highlight the demand for taking adhesive forces into account to measure Young's modulus of soft sticky polymeric substrates in cell–substrate interaction studies.