Poroelastic properties identification through micro indentation modeled by using the proper generalized decomposition

Recently, articular cartilage are being intensively studied to be able to understand their properties and mechanical behavior, in order to be able to create effective replacements. However, these structures are complex and their behavior is not effectively modeled yet. In fact cartilage is a biphasic structure and its interstitial fluid pressurization is the main load bearing phenomenon as well as the main lubricant of the structure. Hertzian rate-controlled micro indentation is one of the common experiments that can be used to identify material properties by comparing to the simulated models. In this work we propose to simulate the micro indentation of cartilage by using a simplified mechanical model combined with the use of the proper generalized decomposition to compute the fluid pressure inside the cartilage calcium tissues.