Nanoindentation of soft solids by a flat punch

Measuring the surface tension and elastic modulus of soft materials and biological tissues under different physiological and pathological conditions is of significance for understanding various phenomena associated with deformation. In this paper, the nanoindentation of a circular flat punch on a soft solid is analyzed with the influence of surface tension. By solving the corresponding singular integral equation, the relation between load and indent depth is obtained. When the radius of the flat punch shrinks to the same order as the ratio of surface tension to elastic modulus, surface tension significantly affects the indentation load–depth relation, which provides a facile method to measure surface tension in soft solids and biological tissues. Graphical Abstract: The nanoindentation of a circular flat punch on a soft solid is analyzed with the influence of surface tension. By solving the corresponding singular integral equation, the relation between load and indent depth is obtained. When the radius of a flat punch shrinks to the same order as the ratio of surface tension to elastic modulus, surface tension significantly affects the indentation load–depth relation, which provides a facile method to measure surface tension in soft solids and biological tissues.