Finite element optimization for estimating homogeneous and inhomogeneous material properties of linear and nonlinear biphasic soft tissues

A knowledge of material properties of cartilage tissue is essential to assess its mechanical function, pathology as well as the mechanics of substitute materials used to replace it. Hence, efficient and reliable tools are needed to accurately characterize the mechanical properties of soft tissue. The objective of this thesis research is to develop a finite element optimization procedure to determine the homogeneous and inhomogeneous (in particular, depth-dependent) material properties of cartilage using experimental data. Cartilage is modeled as a biphasic continuum and its solid phase is taken either linear elastic or hyperelastic. The optimization method is based on a sensitivity analysis where the sensitivity of the FE results to a variation in the material properties is either analytically or numerically evaluated. The material properties are updated based on the sensitivities of the material properties and the difference between the actual experimental data and computational experimental data. The optimization method has been tested in two common experimental configurations of cartilage. For linear elastic tissue, either a linear or a quadratic variation of the material properties have been assumed through the tissue depth, while the hyperelastic tissue properties have been taken homogeneous. The optimization method has been found to be efficient to estimate the material properties both in linear and nonlinear analysis.