Lithium ion battery performance at high charge/discharge rates is largely determined by the ionic resistivity of an electrode and separator which are filled with electrolyte. Key to understand and to model ohmic losses in porous battery components is porosity as well as tortuosity. In the first part, we use impedance spectroscopy measurements in a new experimental setup to obtain the tortuosities and MacMullin numbers of some commonly used separators, demonstrating experimental errors of <8%. In the second part, we present impedance measurements of electrodes in symmetric cells using a blocking electrode configuration, which is obtained by using a non-intercalating electrolyte. The effective ionic resistivity of the electrode can be fit with a transmission-line model, allowing us to quantify the porosity dependent MacMullin numbers and tortuosities of electrodes with different active materials and different conductive carbon content. Best agreement between the transmission-line model and the impedance data is found when constant-phase elements rather than simple capacitors are used. Motivation.-Advanced battery models are a valuable tool for evaluating the performance, safety, and life-time of lithium ion batteries, since they can provide insight into the kinetics and the transport characteristics of batteries, which are not or only partially accessible by experiments. To obtain quantitative and meaningful numerical results, the choice of appropriate physical models and boundary conditions with the corresponding, accurately determined, kinetic and transport parameters are key issues. For numerical simulations of battery systems, the ion-transport model for concentrated electrolyte solutions introduced by Newman et al.1 is frequently used. Since the microscopic geometry of actually used porous electrodes and separators are largely unknown, a homogenization approach is applied for the macroscopic description of porous media. In this case, the influence of the microstructure on the macroscopic behavior is modeled by additional geometric parameters such as the porosity ε and the tortuosity τ. The porosity ε is a well-defined property of a porous medium, which can be determined easily. In contrast, the effective tortuosity of separators and particularly of electrodes are more difficult to quantify, and, to further complicate the matter, many different definitions for the tortuosity τ are used in the literature. Thus, the different tortuosity definitions will be presented prior to reviewing the literature concerned with determining the tortuosity or the effective ionic conductivity of porous battery separators and electrodes.

A fixed-point fluid-structure interaction (FSI) solver with dynamic relaxation is revisited. New developments and insights gained in recent years motivated us to present an FSI solver with simplicity and robustness in a wide range of applications. Particular emphasis is placed on the calculation of the relaxation parameter by both Aitken's ∆ 2 method and the method of steepest descent. These methods have shown to be crucial ingredients for efficient FSI simulations.

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SUMMARYThe coupling of flexible structures to incompressible fluids draws a lot of attention during the last decade. Many different solution schemes have been proposed. In this contribution, we concentrate on the strong coupling fluid-structure interaction by means of monolithic solution schemes. Therein, a Newton-Krylov method is applied to the monolithic set of nonlinear equations. Such schemes require good preconditioning to be efficient. We propose two preconditioners that apply algebraic multigrid techniques to the entire fluid-structure interaction system of equations. The first is based on a standard block Gauss-Seidel approach, where approximate inverses of the individual field blocks are based on a algebraic multigrid hierarchy tailored for the type of the underlying physical problem. The second is based on a monolithic coarsening scheme for the coupled system that makes use of prolongation and restriction projections constructed for the individual fields. The resulting nonsymmetric monolithic algebraic multigrid method therefore involves coupling of the fields on coarse approximations to the problem yielding significantly enhanced performance.

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SUMMARYIn this paper, an approach for three-dimensional frictionless contact based on a dual mortar formulation and using a primal-dual active set strategy for direct constraint enforcement is presented. We focus on linear shape functions, but briefly address higher order interpolation as well. The study builds on previous work by the authors for two-dimensional problems. First and foremost, the ideas of a consistently linearized dual mortar scheme and of an interpretation of the active set search as a semi-smooth Newton method are extended to the 3D case. This allows for solving all types of nonlinearities (i.e. geometrical, material and contact) within one single Newton scheme. Owing to the dual Lagrange multiplier approach employed, this advantage is not accompanied by an undesirable increase in system size as the Lagrange multipliers can be condensed from the global system of equations. Moreover, it is pointed out that the presented method does not make use of any regularization of contact constraints. Numerical examples illustrate the efficiency of our method and the high quality of results in 3D finite deformation contact analysis.

The present work focuses on geometrically exact finite elements for highly slender beams. It aims at the proposal of novel formulations of Kirchhoff-Love type, a detailed review of existing formulations of Kirchhoff-Love and Simo-Reissner type as well as a careful evaluation and comparison of the proposed and existing formulations. Two different rotation interpolation schemes with strong or weak Kirchhoff constraint enforcement, respectively, as well as two different choices of nodal triad parametrizations in terms of rotation or tangent vectors are proposed. The combination of these schemes leads to four novel finite element variants, all of them based on a C 1 -continuous Hermite interpolation of the beam centerline. Essential requirements such as representability of general 3D, large-deformation, dynamic problems involving slender beams with arbitrary initial curvatures and anisotropic cross-section shapes, preservation of objectivity and path-independence, consistent convergence orders, avoidance of locking effects as well as conservation of energy and momentum by the employed spatial discretization schemes, but also a range of practically relevant secondary aspects will be investigated analytically and verified numerically for the different formulations. It will be shown that the geometrically exact Kirchhoff-Love beam elements proposed in this work are the first ones of this type that fulfill all these essential requirements. On the contrary, Simo-Reissner type formulations fulfilling these requirements can be found in the literature very well. However, it will be argued that the shear-free Kirchhoff-Love formulations can provide considerable numerical advantages such as lower spatial discretization error level, improved performance of time integration schemes as well as linear and nonlinear solvers or smooth geometry representation as compared to shear-deformable Simo-Reissner formulations when applied to highly slender beams. Concretely, several representative numerical test cases confirm that the proposed Kirchhoff-Love formulations exhibit a lower discretization error level as well as a considerably improved nonlinear solver performance in the range of high beam slenderness ratios as compared to two representative Simo-Reissner element formulations from the literature.