This thesis is part of the long-term perspective to implement in vivo some new noninvasive methods to monitor the bone prostheses sealing or osseointegration (dental implants, hip prostheses). Although the most widely used clinically, X-ray radiography suffers from low sensitivity, limiting for instance its ability to detect early loosening of a prosthesis. The potential of methods developed over the past twenty years and based on elasticity measurements has been shown in vitro, but their in vivo effectiveness is still questionable. Our objective was to evaluate the potential of new methods based on nonlinear elasticity measurements that have emerged in the fields of geophysics and nondestructive testing, and which showed greater sensitivity than the linear elastic response to the presence of weak contacts within a rigid structure, such as cracks. For this, several osseointegration and sealing models (with manifold damping and boundary conditions) have been studied experimentally using different nonlinear elasticity techniques. Finally, this experimental study allowed the extraction of the most promising nonlinear parameters and the evaluation of their respective advantages and limitations for an in vivo application.
