Surface effects on the spherical indentation of biological film/substrate structures

Abstract

Micro-/nano-indentation has been the most popular technique to extract the mechanical characteristics of biological cells and tissues. However, due to surface effects and existence of substrate, the conventional contact models are unable to determine the accurate elastic modulus of biological samples through analyzing the measured load-indent depth data. In this study, the spherical indentation on the film/substrate structure considering surface energy and large deformation is investigated. The hyperelasticity of biological film and substrate is considered through neo-Hookean constitutive model, and the surface effect is incorporated by finite element method. The explicit formulas of relations between load and indent depth are presented for films with two orders of magnitude modulus mismatch to the substrate. It is found that the modulus mismatch between film and underlying substrate would lead to an overestimation of modulus for the film on a harder substrate, but an underestimated modulus for that on a softer substrate if the conventional Hertzian theory is directly adopted in analysis. Moreover, for indentation at micro-/nano-scale, surface energy would pronouncedly reduce the indent depth under a given load and lead to a seemingly stiffer film. Our results provide the explicit expressions to accurately predict the spherical indentation response of biological film/substrate structures.

Influence of adhesion on oscillatory indentations of viscoelastic biomaterials by a rigid cone

“…Diseases such as cancers and cardiomyopathies are closely correlated with changes in the mechanical properties of cells and tissues, particularly their viscoelastic properties [1][2][3][4][5][6]. Oscillatory indentations by atomic force microscopies (AFM) [7][8][9][10][11][12] are widely adopted to measure the viscoelastic behaviors [13,14].…”