A Hyperelastic Porous Media Framework for Ionic Polymer-Metal Composites and Characterization of Transduction Phenomena via Dimensional Analysis and Nonlinear Regression
Ionic polymer-metal composites (IPMC) are smart materials that exhibit large deformation in response to small applied voltages, and conversely generate detectable electrical signals in response to mechanical deformations. The study of IPMC materials is a rich field of research, and an interesting intersection of material science, electrochemistry, continuum mechanics, and thermodynamics. Due to their electromechanical and mechanoelectrical transduction capabilities, IPMCs find many applications in robotics, soft robotics, artificial muscles, and biomimetics. This study aims to investigate the dominating physical phenomena that underly the actuation and sensing behavior of IPMC materials. This analysis is made possible by developing a new, hyperelastic porous media modeling framework for IPMCs. Using the principles of continuum thermodynamics and multiphasic materials, a finite-strain porous media formulation of IPMC materials is developed. The intricate polymer-electrode interface coupling is extended to such a finite-strain model by accounting for charge conservation at deforming material interfaces. Using this new modeling framework, the effects of kinematic nonlinearity are explored, and a partially linearized kinematic model is proposed for capturing rotational deformation in an otherwise linear model. The most comprehensive dimensional analysis of IPMC transduction phenomena is presented, characterizing the IPMC actuator, short-circuit current, and open-circuit voltage response under static and dynamic loading. The information obtained in this analysis is used to construct nonlinear regression models for the transduction response as univariant and multivariant functions. Automatic differentiation techniques are leveraged to linearize the nonlinear regression models in the vicinity of a representative IPMC description and derive the sensitivity of the transduction response with respect to the driving independent variables. Further, the multiphysics model is validated using experimental data collected for the dynamic IPMC actuator and voltage sensor. With data collected from physical samples of IPMC materials in-lab, the regression models developed under the new computational framework are verified. Using these regression models to interpret the experimental data allowed for further material property characterization to occur, demonstrating the capability of using hybrid computational / experimental regression models to extract information regarding material properties that would otherwise be unknown within the data collected. Key values for the mobile concentration and electric potential fields are approximated using order-of-magnitude arguments and the sharpness of the gradients that occur at the polymer-electrode interfaces of IPMC materials. These values allow for approximate reconstruction of the fields themselves, which in turn are leveraged to formulate the internal bending moments and steady-state curvature of the IPMC. Using both an Euler-Bernoulli beam and a constant curvature arc model for the IPMC, the deformation and rotation of the of the order of magnitude model demonstrated impressive performance for being based on rough approximations. The curled shape of IPMCs under large applied potentials with nonlinear deformation are recovered using this simplified model, and the ability to extend the model for dynamic actuation is outlined
