The thermal behavior of Li-ion cells is an important safety issue and has to be known under varying thermal conditions. The main objective of this work is to gain a better understanding of the temperature increase within the cell considering different heat sources under specified working conditions. With respect to the governing physical parameters, the major aim is to find out under which thermal conditions a so called Thermal Runaway occurs. Therefore, a mathematical electrochemical-thermal model based on the Newman model has been extended with a simple combustion model from reaction kinetics including various types of heat sources assumed to be based on an Arrhenius law. This model was realized in COMSOL Multiphysics modeling software. First simulations were performed for a cylindrical 18650 cell with a $LiCo{O}_2$ -cathode to calculate the temperature increase under two simple electric load profiles and to compute critical system parameters. It has been found that the critical cell temperature $T_{\text{crit}}$ , above which a thermal runaway may occur is approximately $400\mathrm{K}$ , which is near the starting temperature of the decomposition of the Solid-Electrolyte-Interface in the anode at $393.15\mathrm{K}$ . Furthermore, it has been found that a thermal runaway can be described in three main stages.

We prove a Hopf-bifurcation theorem for the vorticity formulation of the Navier–Stokes equations in ℝ³ in case of spatially localized external forcing. The difficulties are due to essential spectrum up to the imaginary axis for all values of the bifurcation parameter which a priori no longer allows to reduce the problem to a finite dimensional one.

Microwave heating is becoming of growing importance in material sciences in the last two decades. Due to the volumetric heating effect, microwave heating offers an energy efficient way of processing materials in several ways. The modeling and simulation of material processing with microwaves with respect to the material structure is a challenging task. The corresponding mathematical modeling results in a coupled, multiscale problem in space and time consisting of Maxwell equations, the heat equation and a temperature-dependent description of the dielectric properties of them material under investigation. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

For the optimization of process chains in sheet metal forming it is required to accurately describe each partial process of the chain, e.g. rolling, press hardening and deep drawing. The prediction of the thickness distribution and the residual stresses in the blank has to be of high reliability, since the subsequent behavior of the semi-finished product in the following subprocesses strongly depends on the process history. Therefore, high-quality simulations have to be carried out which incorporate real microstructural data [1,2,3]. In this contribution, the ferritic steel DC04 is analyzed. A finite strain crystal plasticity model is used, for the application of which micro pillar compression tests were carried out experimentally and numerically to identify the material parameters of DC04. For the validation of the model, a two-dimensional EBSD data set has been discretized by finite elements and subjected to homogeneous displacement boundary conditions describing a large strain uniaxial tensile test. The results have been compared to experimental measurements of the specimen after the tensile test. Furthermore, a deep drawing process is simulated, which is based on a two-scale Taylor-type model at the integration points of the finite elements. At each integration point, the initial texture data given by the aforementioned EBSD measurements is assigned to the model. By applying this method, we predict the earing profiles of differently textured sheet metals. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)