Analytical and experimental multiphysics model for biaxial bending and torsion in IPMC actuators considering electric field dependence

Ionic polymer–metal composites (IPMCs) are attractive electromechanical materials for soft robotics and smart actuation due to their large deformation capability under low voltages. However, undesired lateral bending and torsional deformation under electrical excitation significantly limit motion accuracy and efficiency. This paper develops an analytical energy-based model to describe biaxial bending and torsion in IPMC beams using the Euler–Bernoulli beam theory. The formulation is coupled with Poisson–Nernst–Planck equations to capture ion redistribution, time-dependent effects, and electric-field-induced variations in Young’s and shear moduli. Compared to prior PNP-based models with constant moduli or heavy 3D solvers, the proposed formulation is analytical and design-oriented for fast electrode-pattern optimization. By imposing a symmetric electric field distribution and appropriate boundary conditions, parasitic bending and torsion are significantly reduced, leading to lower strain energy. The analytical results indicate a linear longitudinal bending response and a nonlinear, field- and time-dependent transverse behavior. Experimental validation using fully coated and patterned (strip-electrode) IPMC samples confirms substantial torsion reduction and improved motion stability in the patterned configuration.