A multibody approach to the contact dynamics: a knee joint application

In this thesis, a general approach for dynamic analysis of multibody systems with contact is presented, being a special attention given to the articular contact at the human knee joint. Two methodologies, in two- and three-dimensions, for knee contact modeling are proposed under the framework of multibody systems using generalized Cartesian coordinates. The development of the planar multibody knee model encompasses four steps: (i) geometrical representation of contacting profiles by means of curve fitting techniques based on spline interpolation functions; (ii) location of contact points and evaluation of the contact indentation; (iii) calculation of the contact forces by using an appropriate constitutive law; (iv) description of the ligament behavior by a quadratic stress-strain relation. The motion of the tibia relative to the femur is modeled combining the action of the knee ligaments with the potential contacts between the bones. The contact forces, together with the forces produced by the ligaments, are introduced into the Newton-Euler equations of motion as external generalized forces. Within the three-dimensional methodology, the contact surfaces are described by means of point-clouds extracted from parametric representations. The spatial formulation presents a pre-processing unit. This preprocessor allows for a significantly reduction of the amount of memory required for data storage and an improvement of the computational efficiency of the contact detection process. Computational simulations were performed with the aim of validating both proposed approaches, two-dimensional and three-dimensional. The behavior of the planar knee model resultant of the application of different contact force laws was studied. Moreover, the influence of the geometric and material properties on the dynamic response of the knee joint model was investigated. In a broad sense, the proposed methodologies demonstrated to be suitable for the analysis of the dynamic behavior of multibody models with contact, especially those ...