Evaluation of thickness and Young's modulus of soft materials by using spherical indentation testing

Spherical indentation testing is a minimally invasive technique that can be used instead of highly invasive techniques such as tensile to measure the deformation behavior of various materials. Due to this characteristic, it is useful for evaluating the mechanics of human tissues because in vivo measurements can be performed easily. However, the large deformations that are caused by indentations lead to significant errors in the results evaluation by the Hertz theory, which is reliable in the case of the small deformation conditions. In this paper, spherical indentation testing is studied to evaluate the dimension and rigidity of soft materials such as biological soft tissues. Here, the Hertz theory is functionally expanded to evaluate indentations for soft materials, which undergo large deformations. In the expansions, the technique used for evaluating the thickness of finite specimens is first explained by alalyzing the experimental results of indentations. Then, the Young's modulus of soft materials with finite thickness is theoretically derived by defining an equivalent indentation strain for the analysis of the indentation process. The expansions are examined to evaluate its reliability by applying them to measure the thickness and Young's modulus of sheets of Polyurethane resin.