Large Deformation Modeling of McKibben Actuators with Helical Inextensibility and End Effects

Abstract McKibben actuators are soft pneumatic artificial muscles comprising a hyperelastic tube constrained by a nearly inextensible helical braid. This work develops an axisymmetric continuum formulation for a pressurized hyperelastic tube, incorporating braid inextensibility through a weak constraint applied at the outer surface. The formulation is implemented within an axisymmetric finite element framework and compared with a reduced-order analytical model based on an axially uniform deformation assumption. The results demonstrate that geometric end effects, neglected in reduced-order models, play a significant role in the nonlinear pressure–stretch response, particularly for actuators of finite length. The model achieves improved predictive accuracy over reduced-order approaches while remaining computationally efficient compared to detailed three-dimensional finite element models that explicitly resolve braid–tube contact. The finite element predictions agree well with experimental results from different sources and capture features not reproduced by the analytical model. Discrepancies often attributed to friction are shown to arise primarily from the omission of end effects.