02 Fakultät Bau- und Umweltingenieurwissenschaften
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Item Open Access Simulation of charged hydrated porous materials(2009) Acartürk, Ayhan Yusuf; Ehlers, Wolfgang (Prof. Dr.-Ing.)It is the goal of this work, to understand the behaviour of charged, hydrated, multiphasic materials and to find a thermodynamically consistent model, in order to perform realistic numerical simulations. Hydrated, porous materials are build up of several constituents, i. e., they consist of a charged solid skeleton and a moving interstitial viscous pore-fluid. The pore-fluid itself is composed of the solvent and the ions of a dissolved salt. Due to this special structure such materials answer with swelling and shrinking processes to electrical fields and to changes of the chemical composition of their environment. These materials occur in both the geomechanics as well as biomechanics. As examples for geomechanical materials clay and shale are mentioned and for biomechanical ones the soft biological tissues, i. e., articular cartilage and the inner core of the intervertebral disk, the Nucleus Pulposus, are mentioned. As described above, these materials have a complicated microstructure. Such a microstructure can be described best by a continuum-mechanical model. Thus, the present thesis is based on the macroscopic Theory of Porous Media (TPM). After a short introduction to the topic of the charged, hydrated porous materials, the fundamental concepts of the TPM are briefly discussed. After this general part valid for all multiphasic continua, the axiomatically introduced balance equations are adapted to the given situation, i. e., the regarded continuum consists firstly of two unmiscible phases, the solid skeleton and the pore-fluid and, secondly, the pore-fluid itself is build up of miscible components, the solvent and the solutes. Moreover, the two strong restrictions on the overall aggregate, i. e. the saturation condition and the electroneutrality condition are incorporated into the entropy inequality by use of Lagrange multiplicators. Subsequently, the entropy inequality is evaluated. By this approach it is guaranteed that the constitutive assumptions do not contradict the entropy inequality. The result is a model, wherein the solid deformation is described on the basis of a Neo-Hookean law, the pore-fluid motion on the basis of an extended Darcy equation, the ion diffusion on the basis of an extended Nernst-Planck equation and the electrical potential by the Poisson equation. The governing set of partial differential equations (PDE) is solved in the frame of the finite element method (FEM). Therefore, the initial and the boundary conditions for the individual partial differential equations (PDG) are discussed. On closer inspection, it is noticeable that for the solution of the PDE different primary variable sets can be chosen. The corresponding sets of equations sets are discussed and the respective pros and cons are put out. Likewise, possible simplifications are discussed, where, by special assumptions, the number of primary variables and, thus, the number of equations to be solved may be reduced. Moreover, depending on the choice of the primary variable set, the boundary conditions depend on the current state of the domain. Such boundary conditions are also known in the area of free surface flows and, also, in fluid-structure interaction. The Dirichlet boundary conditions of these equations need to be fulfilled weakly. Subsequently, simulations are carried out on the basis of the model deduced in this work. In a first step, the different primary variable sets are examined numerically regarding accuracy and stability. It shows up that the primary variable set with most weakly fulfilled boundary conditions is to be preferred. In order to demonstrate the abilities of the model, three-dimensional simulations of a swelling hydrogel cylinder showing finite deformations and a gripper made of an electroactive polymer (EAP) bending under an electric field are shown. Finally, it may be concluded that the model based on the overall pressure and the molar concentration is to be preferred, although this formulation means a higher programming effort. This set of primary variables is numerically more stable and much faster than the other ones.