Analytical relationships for nanoindentation-based estimation of mechanical properties of biomaterials

Nanoindentation is an (almost) non-invasive method for obtaining material properties of different types of materials from the interpretation of experimental data related to indenter load (P) and penetration depth (h). In most cases, the material properties that are obtained by nanoindentation are elastic modulus (E), shear modulus (G) and hardness (H). The main advantages of this method are that no extensive preparation of the test specimen is required and that the mechanical properties can be probed at small scales. Moreover, nanoindentation test procedure is automated and the test equipment is easy to use. In this paper, we review different analytical methods that could be used for obtaining the mechanical properties of biomaterials based on the force-displacement curves generated by nanoindentation machines. Some practical issues including different types of machines and tips, calibration of nano-indentation machines, sources of error and specimen preparation are also briefly discussed. The main interest of this paper is the elastic behavior of biological tissues and biomaterials. Nevertheless, there is one section on elasto-plasticity, because purely elastic deformation of linearly elastic materials is difficult to achieve. The analytical solutions found in the literature for different material models are presented including the relationships found for linear elastic, elasto-plastic, hyperelastic, viscoelastic and poroelastic materials. These material models are relevant material models for studies of biological tissues and biomaterials.