On variable stiffness of flexible parallel electroadhesive structures

Electrostatic layer jamming represents a lightweight, low energy consumption, electrically tunable, and cost-effective variable stiffness structure. Flexible parallel electroadhesive structures are the simplest form of electrostatic layer jamming. There is a lack of comprehensive and experimentally validated theoretical variable stiffness models of flexible parallel electroadhesive structures. Here we present the first variable stiffness model of flexible parallel electroadhesive structures under three-point bending, cantilever beam bending subjected to tip concentrated forces, and cantilever beam bending subjected to uniformly distributed forces, using the Euler–Bernoulli beam theory and considering friction and slip between layers by integrating the Maxwell stress tensor into the model. We find that: (1) three-point bending and cantilever beam bending under tip concentrated forces only have pre-slip and full-slip, whereas cantilever beam bending under uniformly distributed forces has an additional partial-slip which can be used for stiffness modulation; (2) the stiffness during the pre-slip stage is four times larger than the stiffness in the full-slip stage; and (3) increasing the voltage, dielectric permittivity, and coefficient of friction can elongate the pre-slip stage, thus enhancing the structural load capability. A customized three-point bending and a cantilever beam bending experimental setup were developed and the experimental deflection–force curve agreed relatively well with the theoretical one. The model, which considered electrode thickness and Young’s modulus, and the results presented in this work are useful insights for understanding the variable stiffness mechanism of electroadhesive layer jamming and are helpful for their structural optimization towards practical applications.