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This is part 3 of a multi-part series which goes through the custom joint replacement to a finger due to rheumatoid arthritis.

Part 1 Scan data to CAD

Part 2 CAD to FEA

Part 3 FEA to Fatigue

Durability Analysis (fe-safe/Rubber)

The two silicone variants reported in Leslie et al (2008) are compared to show how different grades of silicone with similar hyperelastic material properties (herein assumed identical) can influence the fatigue life of a device.

In addition to the hyperelastic properties already given, the fatigue crack growth rate law and initial crack precursor size (ie flaw size) were specified. The Thomas (1958) crack growth rate law was utilized, since the data from the Leslie (2008) results closely fit this model. Both materials have a critical fracture strength Tc of approximately 15 kJ/m2. The materials differ strikingly, however, in their powerlaw slope F0, as shown in the plotted crack growth rate curves in Figure 18. Because silicone is an amorphous elastomer, no strain crystallization is specified.

The crack precursor size was calibrated, using fe-safe/rubber’s flaw size calibration feature, in the present case to give a similar strain-to-rupture for both silicones – roughly 350%-400%. The crack precursor size of an elastomer reflects the worst case microscopic flaws existing in the material. Such flaws have been shown to arise both from sources intrinsic to the rubber compound (ie polymer and recipe) and from extrinsic sources introduced via mixing (ie dispersion of particulate constituents), contamination or processes that result in porosity (ie inadequate degassing). A review of past studies indicates that precursor sizes in the range from 2 to 200 microns can be expected.

Table 1 gives the values of all crack growth parameters used in the model.  The results plotted in Figures 19 and 20 have been computed using fe-safe/Rubber from the given material properties.  Figure 19 shows the strain-life curve for each material. Figure 20 shows the Haigh diagram for each material.

Thomas Silicone-A Silicone-B
FLAWSIZE 0.0273 (mm) 0.0134 (mm)
FLAWCRIT 1 (mm) 1 (mm)
RC 5.46e-4 (mm/CYCLE) 5.46e-4 (mm/CYCLE)
TCRITICAL 15 (kJ/m^2) 15 (kJ/m^2)
F0 1.29 2.54

Table 1 Hyperelastic Ogden material model for Silicone-A and Silicone-B where the bolded properties indicate differences

Figure 1: Fatigue Crack Growth curve plots of Silicone-A and Silicone-B

Figure 2: Strain life curve – simple tension of Silicone-A and Silicone-B

Figure 3: Haigh Diagram Silicone-A and Silicone-B. Blue contours indicate long fatigue life, red contours indicate short life. Contour label values give the base 10 log of the fatigue life (example: 3 = 103 = 1000 cycles).

The duty cycle of the implant consists in flexing between the 20° and 70° positions. For purposes of analysis, the motion was discretized in 10° increments. The 6 components of the 3D strain tensor, along with the hydrostatic pressure, were imported to fe-safe/Rubber from the Abaqus ODB file for each element of the model.

Figure 4: Time history of 1 duty cycle

The strain history in each element of the finite element model is generally multiaxial in nature.  Accordingly, fe-safe/Rubber’s Critical Plane Analysis is required in order to accurately assess durability.  Critical Plane Analysis assumes that a crack precursor may be oriented in any direction, and that therefore a search is required to determine which crack orientation maximizes the rate of crack growth.  The crack orientation that maximizes the crack growth simultaneously minimizes fatigue life, and is called the Critical Plane.  The fatigue life associated with the Critical Plane is computed and reported for each element, and is then plotted to determine locations on the implant where failure will occur.

Results

The initial FEA simulation strain plots are given below for both 20° extension and 70° flexion. Through the fatigue cycle data has been reported for every 10°. In figure 22 the strains have been plotted for the device along with the maximal strain locations for 20° extension and 70° flexion. Figure 23 shows the fatigue life for the device with both silicone-A and Silicone-B. Silicone A has a fatigue life of 1e11 which is higher than the required 1e7, however, with Silicone-B the fatigue life is infinite with no fatigue damage. Also of note is that the maximal strains are not located at the same location as the minimal fatigue life.

Figure 5: Strain plot under 20° extension and 70° flexion

Figure 6: Device only strain plot under 20° extension and 70° flexion with maximal strain locations

Figure 7: Fatigue life for Silicone-A 11.0578 Loglife-Repeats with minimal life location, Silicone-B has an infinite fatigue life

The predicted direction of crack initiation in the implant can be determined by outputting the damage sphere from fe-safe/Rubber. The damage sphere shows the results of the critical plane analysis on a sphere where each point represents the endpoint of a different unit normal vector.  The endpoint of each unit vector is colored according to the fatigue life of the associated crack orientation.  The damage sphere is oriented relative to the local element coordinate system, and indicates which loading directions are most responsible for damage occurring at that location in the implant. Based on the damage sphere the fatigue life is dominated by tension in the distal stem.

Figure 8: Damage sphere from fe-safe/Rubber: locations of: 20° max strain, 70° max strain and minimum fatigue life

Conclusion

This simulation started with a patient-specific CT scan of the hand which is parsed by density to isolate the bone tissue from the soft tissue. From here CAD geometry was created that matched the neutral hand position of the scan along with a proposed surgical technique. A non-linear finite element model was created that included large deformation, contact and a 3rd order Ogden hyperelastic material properties. These results were imported into the fe-safe/Rubber durability calculation with a non-crystallizing Thomas law. From here a non-parametric shape optimization was performed to increase the device’s fatigue life.

References

  1. Swanson Surgical Technique http://www.wmtemedia.com/ProductFiles/Files/PDFs/010500_EN_HR_LE.pdf
  2. Visible Korean http://vkh3.kisti.re.kr/?q=node/24
  3. Cortical bone modulus https://www.ncbi.nlm.nih.gov/pubmed/8429054
  4. Support for 10 million cycles through 90 degrees of flex. https://www.accessdata.fda.gov/cdrh_docs/pdf/K970544.pdf
  5. Silicone material properties http://www.sciencedirect.com/science/article/pii/S2214963514000480
  6. Leslie, Laura, Stephen Kukureka, and D. E. T. Shepherd. “Crack growth of medical-grade silicone using pure shear tests.” Proceedings of the Institution of Mechanical Engineers, Part H: Journal of Engineering in Medicine 222, no. 6 (2008): 977-982.
  7. Thomas, A. G. “Rupture of rubber. V. Cut growth in natural rubber vulcanizates.” Journal of Polymer Science Part A: Polymer Chemistry 31, no. 123 (1958): 467-480.

Acknowledgements

  1. Kerim Genc and Thomas Spirka (Synopsys) for providing processed CT data and scan visualization guidance.
  2. Will Mars and Mark Bauman (Endurica) for providing material properties and fatigue modelling guidance.

This is part 3 of a multi-part series which goes through the custom joint replacement to a finger due to rheumatoid arthritis.

Part 1 Scan data to CAD

Part 2 CAD to FEA

Part 3 FEA to Fatigue