Prof Alvo Aabloo, PhD, University of Tartu
Prof Kwang J. Kim, PhD, University of Nevada, Las Vegas
Prof Barbar Akle, PhD, Lebanese American University
Prof Mart Min, PhD, Tallinn University of Technology
Ionic polymer-metal composites (IPMC) have been studied during the past two decades for their potential to serve as noiseless mechanoelectrical and electromechanical transducers. The advantages of IPMC over other electroactive polymer actuators are low voltage bending, high strains (>1%), and an ability to work in wet environments. The main focus has been on the electromechanical transduction property - the material's ability to exhibit large bending deformation in response to a low (typically 1...5 V) applied voltage. However, lately research on the mechanoelectrical transduction properties of the material has gained more attention. In order to describe both deformation in response to applied voltage (electromechanical transduction) and induced voltage in response to applied deformation (mechanoelectrical transduction) properties of IPMC, an advanced physics based model of the material is necessary. Ongoing research has been focused on creating such model where real measurable quantities can be imposed as boundary conditions in order to reduce the number of unknown parameters required for calculations. In this dissertation, a physics based model that is based on novel hp-FEM (finite element method) is proposed. From the fundamental aspect, previously proposed and validated physics based model consisting of a system of Poisson-Nernst-Planck-Navier's equations is described in detail and used in IPMC deformation calculations. From the mathematical aspect, a novel hp-FEM method was researched to model the equations efficiently. The main focus of this disseration is on the mathematical aspect. Full derivation of the equations with an in-depth study of the benefits of using higher order FEM with automatic adaptivity is presented. The explicit weak form of the Poisson-Nernst-Planck system for Newton's method is presented. Thereafter, a brief overview of the adaptive multi-mesh hp-FEM is introduced and the residual vector and Jacobian matrix of the system is derived and implemented using hp-FEM library Hermes. It is shown how such problem benefits from using individual meshes with mutually independent adaptivity mechanisms. To begin with, a model consisting of only the Poisson-Nernst-Planck system is solved using different adaptivity algorithms. For instance, it is demonstrated that the problem with set of constants that results Debye's length in the nanometer scale can be successfully solved. What makes it even more remarkable is the fact that the calculation domain size is in the millimeter scale. Based on those results, the complete Poisson-Nernst-Planck-Navier's system of equations is studied for IPMC electromechanical transduction calculations. Again, the entire mathematical derivation including weak forms, the residual vector and Jacobian matrix are presented. Thereafter, a number of simulations are analyzed in terms of problem size and consumed CPU time. The best automatic adaptivity mode for such problem is determined. It is also shown how hp-FEM helps to keep the problem geometrically scalable. Additionally, it is demonstrated how employing a PID controller based time step adaptivity helps to reduce the total calculation time. Overall, by using hp-FEM with adaptive multi-mesh configuration the Nernst-Planck-Poisson-Navier's problem size in IPMC deformation calculations is reduced significantly while a prescribed precision of the solution is maintained.