Technical Report 2009-02 A Cosimulation Approach for the Time Analysis of a Biomechanically-Inspired System with Rigid and Deformable Bodies

The goals of this study were to develop a simplified finite element knee model, cosimulate this model with the motion of knee flexion/extension to demonstrate the concept of cosimulation, and choose an integrator to maximize the efficiency of the cosimulation process. A simplified model of the knee was used to simulate flexion/extension in FEBio. The femur was modeled as a fixed, rigid body, the knee complex soft tissue, and the tibia/fibula complex as a rigid body with prescribed motion to rotate about the knee center. Both a fourth order Runge-Kutta (RK4) integrator and Hilber-Hughes-Taylor (HHT) integrator were used to solve for rigid body dynamics in Matlab. Both the RK4 and HHT integrators produced the same angular position time trace for each damping situation but did not use the same time steps. For the underdamped system, RK4 was faster. However, as damping ratio increased, RK4 needed smaller step sizes to maintain stability and therefore became slower that HHT.