## 2 Materials and Methods
### Model Development  
The tendon thicknesses 'e' was applied to the bulk dielectric at the device's edge and was set to 50 \(\upmu\)m. The space between the plates and the air gaps, 'w3', was nominally 50 \(\upmu\)m but was swept to determine its relationship with force output. The top and bottom edge thickness 'c' was kept fixed at 50 \(\upmu\)m. The width of the electrode plates in both the x and y directions was defined by 'w1' and set at 400 \(\upmu\)m. The electrode plate thickness and spacing in the z-direction 't' was defined as 100 \(\upmu\)m. The small width of the air gap, 'w2', was nominally 50 \(\upmu\)m but was swept to determine its relationship with force output. The long width of the air gap was the same as the plate width, 'w1'. The parameters are shown below in Figure 1 showing the geometry in side view. Three physics nodes were utilized: electrostatics, solid mechanics, and laminar flow. The solid mechanics node was applied to the bulk dielectric, the moving mesh node to the electrode chambers along with the air gaps, and the electrostatics node was applied to all domains. To correlate the nodes and affect actuation on the model, the electromechanical forces and fluid-structure-interaction nodes were applied to the model. To properly define the properties of the model, the following materials from the COMSOL material library were applied to specific areas. PDMS was applied to the bulk dielectric of the actuator (shown in orange in Figure 1), water was applied to the electrode plates (shown in blue and red in Figure 1), and air was applied to the air gaps (shown in green in Figure 1). A potential of 3000 V was applied to all surfaces of one set of electrodes, while a ground potential was applied to the other set. The potential was applied to the model using a ramp function. The ramp function improved convergence significantly during the simulation. This voltage was chosen to ensure that any electrostatically induced deformation would not exceed the dielectric breakdown threshold of PDMS. Figure 2 displays how the electric potential was applied to the model (blue plates represent electrodes with electric potential and red plates represent ground). Dielectric properties were applied to  
Figure 1: Gap simulation model showing geometric parameters (side view). Electrodes are represented in blue (positive bias) and red (ground). Air gaps are shown in green. The bulk material is shown in orange. the different domains using the charge conservation node, which applied properties based on their respective materials. The mesh developed for the model can be separated into two regions: the bulk dielectric and the air gaps. The model mainly uses a quadratic tetrahedral element excluding the air gaps, which instead use linear tetrahedral elements for computational efficiency for the fluid flow simulations. The bulk dielectric uses a minimum element size of 10 \(\upmu\)m. The air gaps use a minimum element size of 3 \(\upmu\)m. This smaller minimum mesh size for the air gaps is to ensure appropriate mesh densities for the smaller geometries of the model. The air gaps also featured a layered prism mesh along the faces of the air gaps and pdms boundaries to ensure proper simulation of the no-slip boundary condition. The mesh element dimensions were held constant during parameter-sweep simulations, and the values were determined, due to offering both computational efficiency and accuracy, while optimizing model convergence. A fixed-boundary node was applied to the top and bottom faces of the bulk dielectric. In a practical application, the muscle would be attached on each end to rigid non-slip plates interfacing with the outside world. That condition is fairly represented by the boundaries chosen herein. The material was defined as linear elastic for the purpose of this simulation. Figure 3 displays the solid mechanics boundary conditions in black hashes on the top and bottom face of the model. These boundary conditions are analogous to applying a tensile load on a cantilever beam.