Nonlinear dynamics of an artificial muscle with elastomer–electrode inertia: Modelling and analysis

Artificial muscles are dielectric elastomeric system that mimic the response of the natural muscle and are helpful in many bio-mimicking applications. The existing literature is based on the assumption that electrodes are compliant and are focused on materials with greater extensibility than biological matter. The present work deals with the modelling and nonlinear dynamic analysis of dielectric elastomers considering the elastomer–electrode inertia and damping effect for bio-mimicking. The distinguishing point of the proposed work is the appearance of terms related to the elastomer–electrode inertia effect in the governing equation. Further, the biological muscle’s nonlinear elastic behaviour is incorporated using the Fung material model. Equilibrium stretch variation with parameter exhibits cusp catastrophe. The effect of electrode inertia on the equilibria is examined. Single-well and double-well potential energy characteristics are obtained for constant voltage. The basin of attraction illustrates the sensitiveness of system dynamics on the initial state and damping. The system response, when subjected to time-varying voltage, is explored. Multi-frequency response exists due to harmonic, sub-harmonic, and super-harmonic resonance condition. The resonant frequency variation with geometry and inertia is presented. Time-varying voltage may lead to chaotic behaviour illustrated through the bifurcation diagram. The presence of a strange attractor and positive Lyapunov exponent in the chaotic region further justify the existence of chaos. Additionally, chaotic behaviour is obtained in the case of single-well and double-well potential. Also, the existence of similar attractors with same fractal dimension is shown. The inertia effect significantly changes the dynamic characteristic from chaotic to non-chaotic or vice-versa. The mechanical and electrical load may lead to chaotic or non-chaotic behaviour depending on the geometry of the elastomer. The chaotic region’s dependence on the damping value is also obtained. Our results show that electrode inertia significantly impacts the elastomer under quasi-static and dynamic conditions. The proposed work gives a foundation for precisely designing artificial muscle for practical applications like soft robotics, artificial arms, and different prosthetic implants.