Virtual Power Based Algorithm for Decoupling Large Motions from Infinitesimal Strains: Application to Shoulder Joint Biomechanics

Abstract

New trends of numerical models of human joints require more and more computation of both large amplitude joint motions and fine bone stress distribution. Together, these problems are difficult to solve and very CPU time consuming. The goal of this study is to develop a new method to diminish the calculation time for this kind of problems which include calculation of large amplitude motions and infinitesimal strains. Based on the Principle of Virtual Power, the present method decouples the problem into two parts. First, rigid body motion is calculated. The bone micro-deformations are then calculated in a second part by using the results of rigid body motions as boundary conditions. A finite element model of the shoulder was used to test this decoupling technique. The model was designed to determine the influence of humeral head shape on stress distribution in the scapula for different physiological motions of the joint. Two versions of the model were developed: a first version completely deformable and a second version based on the developed decoupling method. It was shown that biomechanical variables, as mean pressure and von Mises stress, calculated with the two versions were sensibly the same. On the other hand, CPU time needed for calculating with the new decoupled technique was more than 6 times less than with the completely deformable model.