Abstract
In finite element (FE) analysis of long bones it is now common practice to calculate the material properties based on CT data. Although a unique material property is calculated for each element, assigning each element an individual material property results in excessively large models. To avoid this, it is usual to group the elements based on their material properties and to assign each group a single material property (Zannoni 1998). No study has analysed the effect the number of material properties used in a long bone FE model has on the accuracy of the results.
The aim of this study was to evaluate the variation in the calculated mechanical environment as a function of the number of material properties used in an FE model.
An FE mesh of a cadaveric human tibia containing 47,696 ten-node tetrahedron elements and 75,583 nodes was created using CT scans. Material properties were calculated for each element of the mesh based on previous work (Rho 1995, 1996). Eleven FE models were created by varying the number of groups (1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024) the elements were divided into. A single material property was assigned to each group. All models were subject to an axial point load of 300N applied on the medial condyle of the tibial plateau while the distal end was fixed. The variation in maximum and minimum principal strains and deflections, at 17 well distributed surface nodes and at 65 randomly distributed nodes within the bone were plotted against the number of element groups. The total strain energy was also plotted against the number of groups. The errors for strain, deflection, and total strain energy were calculated for each model assuming that the model using 1024 element groups was accurate.
The parameter to converge with the least number of element groups was the total strain energy. At 512 element groups the error was less than 0.001% (0.7% for the two material model). The next to converge were the displacements. Using 512 materials the maximum error in displacement at the surface nodes was 0.001% (4.7% for the 2 material model), while for the internal nodes the maximum error was 0.53% (36.7% for the 2 material model). The least convergence occurred for principal strains. The maximum errors when 512 materials were used were 1.06% (57.7% for the 2 material model) and 3.02% (104.5% for the 2 material model) for the surface and the internal nodes respectively.
This study demonstrates the relationship between the accuracy of calculated mechanical environment and the number of material properties assigned to the model. While this study will allow the analyst to make an informed decision on the number of material properties for modelling the human tibia it also helps examine the validity of previous studies which, usually due to limited resources, used fewer material properties.
Correspondence should be addressed to: EFORT Central Office, Technoparkstrasse 1, CH – 8005 Zürich, Switzerland. Email: office@efort.org
