Appendix 2. the Details of the FEA Study

Appendix 2. The details of the FEA study

Meshing:

The CAD geometries of all four stems (normal stem with sharp transition, chamfer or taper, filleted transition, and two-piece (separate pieces connected by Morse taper) were meshed in the Hypermesh pre-processing software. Type of element: 20 noded Hexahedron, Order: Second, Density: 2 to 10 elements per cross sectional edge.

Fig A1: Variance in mesh density used for stems

Materials Properties:

The stems used for testing were manufactured from medical grade stainless steel 316, whose properties are taken from standard technical literature.

Young's modulus = 200 GPa

Density = 8.00 gm/cm3

Poisson's ratio = 0.30

Linear elastic material law is used for the analysis and the material is considered to be isotropic.

Fig A2: Boundary condition used for analysis

Boundary Conditions:

The built in valgus angle of 50 (similar to natural valgus angle) in most of the prostheses causes the bending of stems. As per ISO 14243 standards, the maximum reaction loading during normal gait is 2600 N. Thus, considering the valgus angle of 50 in the prosthesis, the stem is subjected to a bending force of approximately 225 N, considering the sine component of 2600 N. The worst loading condition for the stem would be when the stem is loosely held in the bone, causing bending of the complete stem. Experimentally, the bending force was replicated by holding the bigger diameter stem base and loading an equivalent force of 360 N to cause the bending moment.

Contact:

The contact in the two piece stem was defined using a FREEZE contact, supported by OptiStruct solver. This contact replicates the real life condition of no motion between the two pieces under the given loading. This contact condition enforces zero relative motion on the contact surface and the contact gap opening remains fixed at the original value and the sliding distance is forced to be zero.

Convergence

A linear static analysis was performed on all the stem geometries using OptiStruct implicit solver (Altair Engineering, Inc, Troy, MI). The convergence study was carried out using the mesh density on the edges of the cross sectional area. All of the results were converging with an increase in density. The optimum density could be chosen between 7-10 elements per edge of the cross section, to obtain satisfactory results. Element density of 10 and more significantly increases the computational time.

(a) Sharp transition stem (b) Chamfer stem

Fig A3: Convergence of predicted strain with increase in element density

Table A1: Predicted strain values showing convergence

Analysis:

The trend of experimental strain values at strain gauge location matches with the strain values predicted by FEM. The experimental values are 19.6% to 27.3% higher than FEM predicted strain values at the location of strain gauge deviate from the experimental value. This may be attributed to the low rigidity of the testing fixture, resulting in higher strain values than actually occurring in the test piece. Another source of error could be the difficulty in exact mounting of the strain gauge.

The maximum strain values predicted by FEA show that plain or sharp transition stem is prone to more failures due to high stress concentration. In contrast, the filleted or chamfered stems will exhibit less failure.

Table A2: Variance between predicted and experimental strain

Sharp Transition / Chamfer / Fillet / Two Piece
Experimental Strain
(at strain gauge) / 970 / 917 / 877 / 979
FEA predicted strain
(at strain gauge location) / 711 / 705 / 705 / 715
Error in prediction
(at strain gauge location) / 26.7 / 23.0 / 19.6 / 27.0
FEA predicted maximum strain (close to strain gauge locations) / 894 / 761 / 802 / 912

Fig A4: Experimental strain measured by strain gauge

Fig A5: FEA predicted strain at the location of strain gauge

Fig A6: FEA predicted maximum strain