Markus Kästner

Isogeometric analysis of the Cahn-Hilliard equation - a convergence study

Herein, we present a numerical convergence study of the Cahn-Hilliard phase-field model within an isogeometric finite element analysis framework. Using a manufactured solution, a mixed formulation of the Cahn-Hilliard equation and the direct discretisation of the weak form, which requires a C 1 -continuous approximation, are compared in terms of convergence rates. For approximations that are higher than second-order in space, the direct discretisation is found to be superior. Suboptimal convergence rates occur when splines of order p = 2 are used. This is validated with a priori error estimates for linear problems. The convergence analysis is completed with an investigation of the temporal discretisation. Second-order accuracy is found for the generalised-α method. This ensures the functionality of an adaptive time stepping scheme which is required for the efficient numerical solution of the Cahn-Hilliard equation. The isogeometric finite element framework is eventually validated by two numerical examples of spinodal decomposition.

Multi-Scale Modelling and Simulation of Textile Reinforced Materials

Novel textile reinforced composites provide an extremely high adaptability and allow for the development of materials whose features can be adjusted precisely to certain applications. A successful structural and material design process requires an integrated simulation of the material behaviour, the estimation of the effective properties which need to be assigned to the macroscopic model and the resulting features of the component.

Fluctuations and differential contraction during regeneration of Hydra vulgaris tissue toroids

We studied regenerating bilayered tissue toroids dissected from Hydra vulgaris polyps and relate our macroscopic observations to the dynamics of force-generating mesoscopic cytoskeletal structures. Tissue fragments undergo a specific toroid–spheroid folding process leading to complete regeneration towards a new organism. The time scale of folding is too fast for biochemical signalling or morphogenetic gradients, which forced us to assume purely mechanical self-organization. The initial pattern selection dynamics was studied by embedding toroids into hydro-gels, allowing us to observe the deformation modes over longer periods of time. We found increasing mechanical fluctuations which break the toroidal symmetry, and discuss the evolution of their power spectra for various gel stiffnesses. Our observations are related to single-cell studies which explain the mechanical feasibility of the folding process. In addition, we observed switching of cells from a tissue bound to a migrating state after folding failure as well as in tissue injury. We found a supra-cellular actin ring assembled along the toroids inner edge. Its contraction can lead to the observed folding dynamics as we could confirm by finite element simulations. This actin ring in the inner cell layer is assembled by myosin-driven length fluctuations of supra-cellular F-actin bundles (myonemes) in the outer cell layer.

Accurate calibration of a fringe projection system by considering telecentricity

Fringe projection systems can be used for the measurement of complex workpiece geometries. Virtual fringe projection systems can be used for the calculation of optimal measurement strategies with respect to criteria like a minimal measurement uncertainty. This is the main field of research of the subproject B5 of the collaborative research centre 489 (CRC 489), funded by the German Research Foundation (DFG). The main task of the subproject is to develop a virtual multisensor assistance system for the calculation of workpiece adapted measurement strategies. This paper focuses on the model and calibration of the used fringe projection sensor. The sensor has to be modelled and the system parameters have to be identified by an accurate calibration procedure. The used fringe projection system has a camera lens with an object-sided telecentricity. Usually, the components projector and camera were described using a pinhole model, which does not reflect the telecentricity. This means, that the existing physical formulations and calibration procedures cannot be used, here. In this paper, the model and calibration strategy for the calculation of the system parameters are described in detail. In order to get a precise simulation model, each intrinsic and extrinsic parameter is considered. To verify the virtual model and the calibration strategy, the calibration was repeated and the standard deviation of the parameters was calculated. Furthermore an optical flat and a groove artefact will be measured and the planarity of the optical flat and the depth of the groove artefact will be determined and compared to the calibrated values.

Computation of Effective Stiffness Properties for Textile-Reinforced Composites Using X-FEM

The macroscopic material behaviour of novel textile-reinforced composites is defined by its constituents (micro-level) and the design of the textile reinforcement (meso-level). Consequently, a multi-scale approach to the prediction of the material behaviour is necessary because only in this vein the adaptability of the textile reinforcement can be used to develop materials whose features can be adjusted precisely to certain applications.

Theoretical models for magneto-sensitive elastomers: A comparison between continuum and dipole approaches

In the literature, different theoretical models have been proposed to describe the properties of systems which consist of magnetizable particles that are embedded into an elastomer matrix. It is well known that such magneto-sensitive elastomers display a strong magneto-mechanical coupling when subjected to an external magnetic field. Nevertheless, the predictions of available models often vary significantly since they are based on different assumptions and approximations. Up to now the actual accuracy and the limits of applicability are widely unknown. In the present work, we compare the results of a microscale continuum and a dipolar mean field approach with regard to their predictions for the magnetostrictive response of magneto-sensitive elastomers and reveal some fundamental relations between the relevant quantities in both theories. It turns out that there is a very good agreement between both modeling strategies, especially for entirely random microstructures. In contrast, a comparison of the finite-element results with a modified approach, which-similar to the continuum model-is based on calculations with discrete particle distributions, reveals clear deviations. Our systematic analysis of the differences shows to what extent the dipolar mean field approach is superior to other dipole models.

Endoscopic geometry inspection by modular fiber optic sensors with increased depth of focus

Within the scope of the Collaborative Research Centre (CRC) Transregio 73 (SFB/TR73) research project, a new kind of micro fringe projection system is being developed. By using flexible imaging fibre bundles, it becomes possible to collect complete data sets of filigree and hardly accessible assembly geometries. The talk presents the principle of the new kind of endoscopic micro fringe projection system and points out its certain advantages. It combines a laser light source with a Digital Mirror Device (DMD), image fiber and advanced micro optics. Thereby a 7.5 times increased depth of focus of 3 mm compared to 0.4 mm with common light sources could be achieved. Preliminary considerations of the optical design, simulation results and the consequential setup are as well shown as measurement results of the current system.

On the Design, Characterization and Simulation of Hybrid Metal-Composite Interfaces

Multi-material lightweight designs are a key feature for the development of innovative and resource-efficient products. In the development of a hybrid composite, the interface between the joined components has to be considered in detail as it represents a typical location of the initialization of failure. This contribution gives an overview of the simulative engineering of metal-composite interfaces. To this end, several design aspects on the microscale and macroscale are explained and methods to model the mechanical behavior of the interface within finite element simulations. This comprises the utilization of cohesive elements with a continuum description of the interface. Likewise, traction-separation based cohesive elements, i.e. a zero-thickness idealization of the interface, are outlined and applied to a demonstration example. Within these finite element simulations, the constitutive behavior of the connected components has to be described by suitable material models. Therefore, inelastic material models at large strains are formulated based on rheological models.

High resolution measurements of filigree, inner geometries with endoscopic micro fringe projection

The paper introduces a new fibrescopic micro fringe projector, showing the special requirements of micro fringe projection in combination with coupling to flexible image fibre bundles. So far performed example applications, such as measurements of deep drawing tools, will be shown and difficulties of certain geometries, such as internal gearing elements with steep flank gradients are discussed. Due to the miniaturization of the fringe pattern into a 2 mm diameter fibre bundle and the decrease of resolution in the bundle, a decrease of contrast has to be accepted. That leads to a fading of the sharp edges of black/white crossovers to sine like characteristics on the detection camera. Methods for the compensation of these artifacts in the beforehand made calibration and during the acquisition of the measurement data will be presented. Fitted applications of the conventional grey code technique will be as well introduced and compared as the developing method of encoded phase shift. In the current state the newly designed fringe projector is connected to a high resolution coordinate measurement machine (CMM). Measurement data and achievable resolutions of the connected systems will as well be presented, giving information about realizable measuring volumes.

Assessment of used turbine blades on and beneath the surface for product regeneration: Generation of a damage model based on reflection, geometry measurement and thermography

A camera with a directional illumination system and a thermography camera with 50 mm optics with inductive excitation system are used in order to gather hints for defects on the surface. Using the directional illumination system each picture with a different illumination angle is a sample of the surfaces reflection distribution of each pixel. Deviation of the surface microstructure directly changes the reflection distribution and points to possible damages.