## FEA results for a diamond shaped pressurized plate of variable dimensions

A finite element analysis of stress within the internal bladder of an artificial muscle actuator (AMA) was performed for a variety of possible combinations of actuator design parameters. The relevant parameters of this segment of the bladder are then the edge length, *EL*, and the braid angle, *\gamma*, as shown in mesh_segment.png. The edge length is a measure of the mesh density and is determined in the manufacturing by setting the distance between subsequent strands. The braid angle is a measure of AMA contraction and thus changes as the AMA is pressurized. In addition to the parameters *EL* and *\gamma*, it is also necessary to consider the wall thickness of the bladder material when determining a proper design to prevent failure. Further, the pressure within the bladder is an important consideration for evaluating the stress within the bladder wall. All of these possible variations makes determination of the failure criteria for the internal bladder of the artificial muscle a difficult problem to evaluate. The complexity of this problem is further increased due to the intricacies of shell mechanics for an irregular shape. To simplify the analysis, the bladder was first divided into the smallest repeated unit which takes the form of a diamond where the sides are defined by the strands of the braided mesh, as shown in mesh_segment.png. A model of this individual unit was developed in the finite element analysis software package, Abaqus Unified FEA (DassaultSystemes). As it is possible that each of these four parameters will vary independently, it is necessary to evaluate all possible combinations. To accomplish this, the input file was scripted (see linked Github repo) using the Python programming language to allow for automation of the job submission process. Briefly, the script was set up to evaluate for six possible edge lengths, six braid angles, five bladder thicknesses, and five internal pressures. This results in a total of 900 possible combinations of these four parameters. The range for each parameter was selected to cover the likely range encountered by the AMA when used for a particular application. For each combination, the script defines the geometry of the bladder segment, applies the boundary conditions and pressure load, and submits the job to the solver.

The model used here assumes that the edges of the bladder segment are fixed in place by the braid strands. This assumption is reasonable as each side of a given segment is shared by adjacent segments which are each subject to the same conditions. Further, this model does not account for any stress relief that may be present due to the diameter of the strands restraining the bladder. This results in the overestimation of the stress within the bladder and thus means that the selection of parameters based on this model will be conservative.

The results from each of the 900 simulations were then stored in individual output files. The result of interest in this case is the maximum stress that occurs in the bladder segment. To extract this information from each of the results files, a post processing script was also written in Python (see linked Github repo) to read the VonMises stress data for each element in the mesh and then find the maximum. This maximum VonMises stress was then written to a text file along with the corresponding values for each of the 900 simulations. This text file represents a four dimensional array that can be used as a lookup table to find the stress corresponding to a given set of input parameters.

The attached file 'bladderStressArray.m' is an example of how the data contained within the text files can be imported to Matlab as a 4D array.

The attached file 'bladderStress.m' can then be used to perform a n-dimensional interpolation across the 4D array to output a value for "stress" given desired input values for edge length, braid angle, bladder thickness, and internal pressure.