Dynamic Response of Paper-Based Bi-Material Cantilever Actuator

Abstract

This work presents a dynamic modeling approach for analyzing the behavior of a bi-material cantilever actuator structure, consisting of a strip of filter paper bonded to a strip of tape. The actuator’s response is induced by a mismatch strain generated upon wetting, leading to the bending of the cantilever. The study delves into a comprehensive exploration of the dynamic deflection characteristics of the bilayer structure. It untangles the intricate connections among the saturation, modulus, hygro-expansion strain, and deflection, while uniquely addressing the challenges stemming from fluid–structure coupling. To solve the coupled fluid–solid differential equations, a combined numerical method is employed. This involves the application of the Highly Simplified Marker and Cell (HSMAC) technique for fluid flow analysis and the Finite Difference Method (FDM) for response deflection computation. In terms of the capillary flow model, the Computational Fluid Dynamics (CFD) simulations closely align with the classical Washburn relationship, depicting the wetted front’s evolution over time. Furthermore, the numerical findings demonstrate that heightened saturation levels trigger an increase in hygro-expansion strain, consequently leading to a rapid rise in response deflection until a static equilibrium is achieved. This phenomenon underscores the pivotal interplay among saturation, hygro-expansion strain, and deflection within the system. Additionally, the actuator’s response sensitivity to material characteristics is highlighted. As the mismatch strain evolving from paper hygro-expansion diminishes, a corresponding reduction in the axial strain causes a decrease in response deflection. The dynamic parameter demonstrates that the deflection response of the bilayer actuator diminishes as dynamic pressure decreases, reaching a minimal level beyond which further changes are negligible. This intricate correlation underscores the device’s responsiveness to specific material traits, offering prospects for precise behavior tuning. The dependence of paper modulus on saturation levels is revealed to significantly influence bilayer actuator deflection. With higher saturation content, the modulus decreases, resulting in amplified deflection. Finally, strong concordance is observed among the present fluidically coupled model, the static model, and empirical data—a testament to the accuracy of the numerical formulation and results presented in this study.