## 2 Model Development
### Model Validation  
The model is validated in three steps. First, the in-line production tests of mechanical uniaxial loading of the blades, as cantilevered beams, are simulated and compared to measured values. This comparison confirms assumptions made on material properties. Second, simulations are done of static toe and heel deflection testing of prosthetic feet and compared to measured values. Herein, the sample foot is rigidly attached to a uniaxial test machine and aligned at a fixed angle, \(-15^{\circ}\) for the heel and \(20^{\circ}\) for the toe, against a free rolling plate. The machine compresses the foot for a set displacement and the resulting force is measured. In this process, the model assumptions on contact and joint element settings between different parts are adjusted. Lastly, the simulation of the roll-over task of the technical specification ISO/TS 16955 [28] is done and compared to measurements for validation of the model. Figure 2 shows the schematic structure of the test equipment and procedure. One investigated cycle consists of the dynamic stance phase of a single step. The foot sample is attached to a rod and force is applied to a ball joint at the other end. The rod and attached foot sample are thus free to rotate around the ball joint. The M-shaped force curve represents the ground reaction force of heel-to-toe walking; see Figure 2b). The maximum force peak is set to 824 N, representing the typical ground reaction force of a 70 kg person walking at normal speed. The sample is pushed vertically down on a rotating table (tilt table). The rotation is constant displacement controlled according to a synchronized profile; see Figure 2c). The heel contact at the start of the cycle is at a \(-20^{\circ}\) decline, rolling over to \(40^{\circ}\) incline and pushing the foot up at the toe. Control functions for force and rotation are defined as per the technical specification [28]. A load cell positioned at 500 mm above the foot (about the height of the anatomical knee joint) on the rod measures the resulting forces and moments. A sequence of the roll-over is shown in Figure 3b). The stance phase time is 0.600 s, corresponding to a 1 s normalized step time. Every-day use ESR prosthetic feet are used with a cosmetic foot shell, made of soft elastomers. The foot shell was excluded in the FE modeling as the visco-elastic member would increase the complexity and reduce reliability of the model. In contrast to the standard [28], the comparison mechanical measurements were also executed without a foot cover to allow for direct comparison. Figure 2: **(a)** Schematic image of the setup in mechanical testing according to ISO/TS 16955. Control functions, **(b)** vertical force on ball joint, and **(c)** rotation of tilt-table, as functions of stance phase time (yellow arrows in **(a)**). These are applied as boundary conditions in the FE model. The heel-to-toe profile of the standard does not fully represent normal walking, as it exaggerates the angle at initial contact and loading response of stance phase, resulting in higher moments and anterior-posterior forces than would be expected from clinical gait analysis results. Results of the roll-over simulations are compared to the mechanical testing and presented in a rotational stiffness curve; see Figure 4. The angular moment in the sagittal plane is calculated for the ankle system in the rotational joint between the main body and top blade. This moment reaction is plotted against the ankle angle, characterizing the rotational stiffness of the ankle system throughout stance phase. In the mechanical testing, the force and moment reaction in the load cell are used to calculate the moment in the ankle joint. The ankle angle is measured between the sole blade and the pylon with a 2D video analyzing software, TEMA (Image Systems, Linkoping, Sweden).