Indentation of a cylinder with different shape of the base into viscoelastic half-space

During developing medical equipment and processing results of experiments on the study of biomaterials, it is necessary to describe the process of interaction of the working tool with soft tissues. With this, it is important to take into account not only the mechanical properties of the tissue under study, but also the technical characteristics of the equipment, such as the shape of the tool surface and the speed of the interaction process. For this purpose, a contact model describing the indentation of an axisymmetric rigid cylinder with different foundation surface shape into viscoelastic half-space at a constant speed was constructed. The theory of linear viscoelasticity was used to describe the mechanical behavior of the half-space. A three-parameter model of a standard viscoelastic body was chosen as a viscoelastic model that defines the type of relaxation function of the half-space material. The distribution of contact pressure under the cylinder surface and the dependence of the applied load on the depth of indentation for various forms of the contact surface of the cylinder were obtained. The influence of the shape of the cylinder base surface, the indentation speed and the relaxation properties of the half-space on the characteristics of the contact interaction was studied. For describing the mechanical behavior of biological tissues, a one-dimensional model of a standard viscoelastic body was also considered. For this simplified model, the distribution of the contact pressure under the surface of cylinder with different shape of the base and the dependence of the applied load on time were also obtained. The results obtained using the continuous model and the one-dimensional model were compared. It was shown when it is more appropriate to use the simplified models to describe the interaction of an instrument with biological tissue.