Effects of grid dimensions on finite element models of an articular surface

Recent activity in finite element analysis of articular joints has emphasized refinements in geometry and material properties. In the implementation of such models, it is necessary to ensure that grid dimensions are optimal for suitable solutions of displacements, strains and stresses. A method of grid optimization was developed to ensure that for typical material properties, finite element models of an articular surface agree with known analytical solutions. The layered axisymmetric model presented by Askew and Mow (J. biomech. Engng 100, 105-115, 1978) was used as a reference. From this reference, an STZ of 0.2 mm, middle and deep zones of 0.8 mm and tidemark region of 0.2 mm were chosen. Cancellous bone was an infinite elastic half space under these layers. Loading was a parabolic distribution over a 10 mm radius having a peak of 1 MPa. Agreement was obtained between analytical solutions and finite element solutions when the finite element model had a radial boundary of 30 mm radius and a bone depth of 32 mm. These results suggested that in models of real joints, care must be taken to ensure the boundaries are reasonably represented and that sufficient bone is modelled for adequate solutions.