Carbon-Fiber Running Prosthesis

1. 1

   Start from the physical test

   Test setup

   The prosthesis is a single curvilinear carbon-fiber blade that replaces both the foot and the distal shank. Every boundary condition in the model mirrors this physical bending-and-compression rig directly, rather than a generic idealization: the socket end couples to a reference point, the plantar end contacts two rigid plates through frictionless contact, and the 3000 N load and 40 mm allowable deflection carry over from the test’s own load and stiffness criteria.

   Axial reference test load

   3000 N

   Laminate

   40 plies, symmetric T300/5208, 8 mm

   Parts

   2: deformable blade shell + rigid ground fixture

   Reference point

   1, kinematically coupled at the socket

   

   

2. 2

   Define the geometry

   Parametric profile

   The free-form CAD blade is reduced, for this analysis, to a single dimensioned profile: a short tapered transition at the proximal (socket) end followed by a continuous run of tangent circular arcs that reproduce the blade’s C/J curvature down to the plantar tip. This parametric definition, not an imported free-form surface, is what was meshed and analyzed in Abaqus.

   Material callout

   T300/5208 CFRP

   Drawing scale

   1:2, all dimensions in mm

   Primary bend radius

   R152.6 mm (two tangent arcs)

   Transition and tip arcs

   R97.4–R100

   

3. 3

   Build the composite shell model

   Abaqus/CAE

   The assembly comprises a deformable composite shell (the blade) and a rigid fixture (the loading and ground-contact plates). The blade is meshed with quadratic, reduced-integration shell elements; the rigid fixture with a coarser linear mesh, since it carries no stress solution of its own.

   Every ply is unidirectional and oriented at 0° along the blade’s curvilinear axis, chosen to maximize axial stiffness since the dominant load path under the reference load runs along the blade’s length. The ply is defined as an orthotropic lamina from properties characterized in-house for this T300/5208 system (E₁ = 131 GPa, longitudinal strength 1448 MPa). The strength is close to the widely used Tsai–Hahn reference value (1500 MPa), while the modulus is below its 181 GPa, which makes the deflection estimate conservative. Loads and restraints mirror the physical rig directly: the load point is free only along the load line, the ground fixture is fully fixed, and the blade’s plantar edge is restrained laterally while free to flex in-plane.

   Parts

   Composite blade shell + rigid ground fixture

   Plies modeled / physical

   20 / 40 (symmetric, 8 mm total)

   Shell element size, blade

   6 mm

   Element

   S8R5, 8-node quadratic shell, reduced integration

   

   

   

   

4. 4

   Read the results

   Abaqus/CAE

   Both governing checks clear their limit with margin under the 3000 N reference load.

   Displacement is probed directly at the loaded reference point: δ_max = 18.8 mm (−18.805 mm at node 441), a smooth, monotonic deflection consistent with a curved cantilever compressed at its loaded end.

   Tsai–Hill is evaluated ply by ply (Abaqus reports its square root as TSAIH, so TSAIH = 1 marks failure). The raw contour peaks, up to 0.448, sit directly at the idealized point-coupling constraint, an artifact of concentrating load through a single reference point rather than a real stress riser. Probing away from that region gives the representative peak of 0.355 used throughout this report, an estimated load margin of about 2.8×.

   Peak vertical displacement

   18.8 mm (of 40 mm)

   Representative Tsai–Hill peak

   0.355 (of 1.0)

   Raw peak at the coupling

   0.448

   Estimated load margin

   ≈2.8×

   

• Done: Reaction forces at both reference points balance the applied load, and the contact solution shows no interpenetration, both standard Abaqus diagnostics.
• Done: The peak Tsai–Hill value is probed away from the coupling singularity (0.355 vs. a raw 0.448) and decreases toward the laminate mid-plane, as expected for combined bending.
• Done: Boundary conditions replicate the physical test rig feature for feature (step 1), validated for setup fidelity.
• Outstanding: a quantitative strain-gauge/DIC comparison against the physical article, and a documented mesh-convergence study, before this model is relied on beyond a structural screening role.

An independent order-of-magnitude check, idealizing the blade as a curved composite cantilever using the ply’s own axial modulus, confirms the FE displacement is dimensionally consistent with the laminate’s stiffness. The blade’s width and curvature profile is now available in parametric form (step 2); completing the full closed-form comparison against it remains near-term follow-on work.

• The 40-ply baseline is likely over-stiff for its job

  The blade uses only 47% of its allowable deflection budget at the reference load. Since stored elastic energy scales with ½Fδ, that’s roughly 28 J stored against about 60 J the same envelope would allow at full deflection, close to twice the recoverable energy per stride for the same peak load. That margin reads as a design opportunity, not just a safety cushion.

• Fatigue life is the next required check, not this one

  This is a single static load case; a running prosthesis sees a ground-contact cycle on every stride, putting it deep into the high-cycle fatigue regime over a competitive career. A dedicated S–N or stiffness-degradation characterization is recommended before any thinner design is finalized.