arXiv subjects

Christoph Meier

Publications and source records attributed to Christoph Meier.

48 records · Page 3Linked to original sources

arXiv2018

Extended Comment on the Article "Consistent Development of a Beam-To-Beam Contact Algorithm via the Curve to Solid Beam Contact - Analysis for the Non-Frictional Case"

In the authors' previous works, novel finite element formulations for the contact interaction of slender beams have been proposed. In their recent article "Consistent Development of a Beam-To-Beam Contact Algorithm via the Curve to Solid Beam Contact - Analysis for the Non-Frictional Case", Konyukhov et al. refer extensively to the aforementioned works by the authors. However, many of these statements turn out to be scientifically incorrect and not only question the quality and correctness of the authors' previous works in a way that is neither objective nor justified but also might cause quite some confusion to researchers in this field. Hence, the authors find it necessary to comment on these statements, disprove them if incorrect, and demonstrate the correctness of the derivations made in their previous works.

cs.CE↗

arXiv2018

Critical Influences of Particle Size and Adhesion on the Powder Layer Uniformity in Metal Additive Manufacturing

The quality of powder layers, specifically their packing density and surface uniformity, is a critical factor influencing the quality of components produced by powder bed metal additive manufacturing (AM) processes, including selective laser melting, electron beam melting and binder jetting. The present work employs a computational model to study the critical influence of powder cohesiveness on the powder recoating process in AM. The model is based on the discrete element method (DEM) with particle-to-particle and particle-to-wall interactions involving frictional contact, rolling resistance and cohesive forces. Quantitative metrics, namely the spatial mean values and standard deviations of the packing fraction and surface profile field, are defined in order to evaluate powder layer quality. Based on these metrics, the size-dependent behavior of exemplary plasma-atomized Ti-6Al-4V powders during the recoating process is studied. It is found that decreased particle size / increased cohesiveness leads to considerably decreased powder layer quality in terms of low, strongly varying packing fractions and highly non-uniform surface profiles. For relatively fine-grained powders (mean particle diameter $17 μm$), it is shown that cohesive forces dominate gravity forces by two orders of magnitude leading to low quality powder layers not suitable for subsequent laser melting without additional layer / surface finishing steps. Besides particle-to-particle adhesion, this contribution quantifies the influence of mechanical bulk powder material parameters, nominal layer thickness, blade velocity as well as particle-to-wall adhesion. Finally, the implications of the resulting powder layer characteristics on the subsequent melting process are discussed and practical recommendations are given for the choice of powder recoating process parameters.

cs.CE↗

arXiv2018

Modeling and Characterization of Cohesion in Fine Metal Powders with a Focus on Additive Manufacturing Process Simulations

The cohesive interactions between fine metal powder particles crucially influence their flow behavior, which is in turn important to many powder-based manufacturing processes including emerging methods for powder-based metal additive manufacturing (AM). The present work proposes a novel modeling and characterization approach for micron-scale metal powders, with a special focus on characteristics of importance to powder-bed AM. The model is based on the discrete element method (DEM), and the considered particle-to-particle and particle-to-wall interactions involve frictional contact, rolling resistance and cohesive forces. Special emphasis lies on the modeling of cohesion. The proposed adhesion force law is defined by the pull-off force resulting from the surface energy of powder particles in combination with a van-der-Waals force curve regularization. The model is applied to predict the angle of repose (AOR) of exemplary spherical Ti-6Al-4V powders, and the surface energy value underlying the adhesion force law is calibrated by fitting the corresponding angle of repose values from numerical and experimental funnel tests. To the best of the authors' knowledge, this is the first work providing an experimental estimate for the effective surface energy of the considered class of metal powders. By this approach, an effective surface energy of $0.1mJ/m^2$ is found for the investigated Ti-6Al-4V powder. This value is considerably lower than typical experimental values for flat metal contact surfaces in the range of $30-50 mJ/m^2$, indicating the crucial influence of factors such as surface roughness and chemical surface contamination on fine metal powders. More importantly, the present study demonstrates that a neglect of the related cohesive forces leads to a drastical underestimation of the AOR and, consequently, to an insufficient representation of the bulk powder behavior.

cs.CE↗

arXiv2017

Non-Markovianity in the optimal control of an open quantum system described by hierarchical equations of motion

Optimal control theory is implemented with fully converged hierarchical equations of motion (HEOM) describing the time evolution of an open system density matrix strongly coupled to the bath in a spin-boson model. The populations of the two-level sub-system are taken as control objectives; namely, their revivals or exchange when switching off the field. We, in parallel, analyze how the optimal electric field consequently modifies the information back flow from the environment through different non-Markovian witnesses. Although the control field has a dipole interaction with the central sub-system only, its indirect influence on the bath collective mode dynamics is probed through HEOM auxiliary matrices, revealing a strong correlation between control and dissipation during a non-Markovian process. A heterojunction is taken as an illustrative example for modeling in a realistic way the two-level sub-system parameters and its spectral density function leading to a non-perturbative strong coupling regime with the bath. Although, due to strong system-bath couplings, control performances remain rather modest, the most important result is a noticeable increase of the non-Markovian bath response induced by the optimally driven processes.

quant-ph↗

arXiv2017

Tunneling induced electron transfer between separated protons

We study electron transfer between two separated nuclei using local control theory. By conditioning the algorithm in a symmetric system formed by two protons, one can favored slow transfer processes, where tunneling is the main mechanism, achieving transfer efficiencies close to unity assuming fixed nuclei. The solution can be parametrized using sequences of pump and dump pi pulses, where the pump pulse is used to excite the electron to a highly excited state where the time for tunneling to the target nuclei is on the order of femtoseconds. The time delay must be chosen to allow for full population transfer via tunneling, and the dump pulse is chosen to remove energy from the state to avoid tunneling back to the original proton. Finally, we study the effect of the nuclear kinetic energy on the transfer efficiency. Even in the absence of relative motion between the protons, the spreading of the nuclear wave function is enough to reduce the yield of electronic transfer to less than one half.

quant-ph↗

arXiv2017

Thermophysical Phenomena in Metal Additive Manufacturing by Selective Laser Melting: Fundamentals, Modeling, Simulation and Experimentation

Among the many additive manufacturing (AM) processes for metallic materials, selective laser melting (SLM) is arguably the most versatile in terms of its potential to realize complex geometries along with tailored microstructure. However, the complexity of the SLM process, and the need for predictive relation of powder and process parameters to the part properties, demands further development of computational and experimental methods. This review addresses the fundamental physical phenomena of SLM, with a special emphasis on the associated thermal behavior. Simulation and experimental methods are discussed according to three primary categories. First, macroscopic approaches aim to answer questions at the component level and consider for example the determination of residual stresses or dimensional distortion effects prevalent in SLM. Second, mesoscopic approaches focus on the detection of defects such as excessive surface roughness, residual porosity or inclusions that occur at the mesoscopic length scale of individual powder particles. Third, microscopic approaches investigate the metallurgical microstructure evolution resulting from the high temperature gradients and extreme heating and cooling rates induced by the SLM process. Consideration of physical phenomena on all of these three length scales is mandatory to establish the understanding needed to realize high part quality in many applications, and to fully exploit the potential of SLM and related metal AM processes.

physics.app-ph↗

arXiv2017

Analysis of the non-Markovianity for electron transfer reactions in an oligothiophene-fullerene heterojunction

The non-Markovianity of the electron transfer in an oligothiophene-fullerene heterojunction described by a spin-boson model is analyzed using the time dependent decoherence canonical rates and the volume of accessible states in the Bloch sphere. The dynamical map of the reduced electronic system is computed by the hierarchical equations of motion methodology (HEOM) providing an exact dynamics. Transitory witness of non-Markovianity is linked to the bath dynamics analyzed from the HEOM auxiliary matrices. The signature of the collective bath mode detected from HEOM in each electronic state is compared with predictions of the effective mode extracted from the spectral density. We show that including this main reaction coordinate in a one-dimensional vibronic system coupled to a residual bath satisfactorily describes the electron transfer by a simple Markovian Redfield equation. Non-Markovianity is computed for three inter fragment distances and compared with a priori criterion based on the system and bath characteristic timescales.

physics.chem-ph↗

arXiv2016

Geometrically exact beam elements and smooth contact schemes for the modeling of fiber-based materials and structures

Recently, the authors have proposed a novel all-angle beam contact (ABC) formulation that combines the advantages of existing point and line contact models in a variationally consistent manner. However, the ABC formulation has so far only been applied in combination with a special torsion-free beam model, which yields a very simple and efficient finite element formulation, but which is restricted to initially straight beams with isotropic cross-sections. In order to abstain from these restrictions, the current work combines the ABC formulation with a geometrically exact Kirchhoff-Love beam element formulation that is capable of treating even the most general cases of slender beam problems in terms of initial geometry and external loads. While the neglect of shear deformation that is inherent to this formulation has been shown to provide considerable numerical advantages in the range of high beam slenderness ratios, alternative shear-deformable beam models are required for examples with thick beams. The current contribution additionally proposes a novel geometrically exact beam element based on the Simo-Reissner theory. Similar to the torsion-free and the Kirchhoff-Love beam elements, also this Simo-Reissner element is based on a C1-continuous Hermite interpolation of the beam centerline, which will allow for smooth contact kinematics. For this Hermitian Simo-Reissner element, a consistent spatial convergence behavior as well as the successful avoidance of membrane and shear locking will be demonstrated numerically. All in all, the combination of the ABC formulation with these different beam element variants (i.e.~the torsion-free element, the Kirchhoff-Love element and the Simo-Reissner element) results in a very flexible and modular simulation framework that allows to choose the optimal element formulation for any given application in terms of accuracy, efficiency and robustness.

cs.CE↗

arXiv2016

Geometrically Exact Finite Element Formulations for Curved Slender Beams: Kirchhoff-Love Theory vs. Simo-Reissner Theory

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 C1-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 or preservation of objectivity and path-independence 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 the considered 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 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.

cs.CE↗

arXiv2016

A Unified Approach for Beam-to-Beam Contact

Existing beam contact formulations can be categorized in point contact models that consider a discrete contact force at the closest point of the beams, and line contact models that assume distributed contact forces. In this work, it will be shown that line contact formulations provide accurate and robust mechanical models in the range of small contact angles, whereas the computational efficiency considerably decreases with increasing contact angles. On the other hand, point contact formulations serve as sufficiently accurate and very efficient models in the regime of large contact angles, while they are not applicable for small contact angles as a consequence of non-unique closest point projections. In order to combine the advantages of these basic formulations, a novel all-angle beam contact (ABC) formulation is developed that applies a point contact formulation for large contact angles and a recently developed line contact formulation for small contact angles, the two being smoothly connected by means of a variationally consistent model transition. Based on a stringent analysis, two different transition laws are investigated, optimal algorithmic parameters are suggested and conservation of energy and momentum is shown. All configuration-dependent quantities are consistently linearized, thus allowing for their application within implicit time integration schemes. Furthermore, a step size control of the nonlinear solution scheme that allows for large displacement increments per time step and an efficient two-stage contact search based on dynamically adapted search segments are proposed. A series of numerical test cases is analyzed in order to verify the accuracy and consistency of the proposed contact model transition regarding contact force distributions and conservation properties, but also for quantifying the efficiency gains as compared to standard beam contact formulations.

cs.CE↗

arXiv2016

A Finite Element Approach for the Line-to-Line Contact Interaction of Thin Beams with Arbitrary Orientation

The objective of this work is the development of a novel finite element formulation describing the contact interaction of slender beams in complex 3D configurations involving arbitrary beam-to-beam orientations. It is shown in a mathematically concise manner that standard beam contact models based on a point-wise contact force fail to describe a considerable range of configurations, which are, however, likely to occur in practical applications. On the contrary, the formulation proposed here models beam-to-beam contact by means of distributed line forces, a procedure that is shown to be applicable for arbitrary geometrical configurations. The proposed formulation is based on a Gauss-point-to-segment type contact discretization and a penalty regularization of the contact constraint. By means of detailed theoretical and numerical investigations, it is shown that this approach is more suitable for beam contact than possible alternatives based on mortar type contact discretizations or constraint enforcement by means of Lagrange multipliers. The proposed formulation is enhanced by a consistently linearized integration interval segmentation avoiding numerical integration across strong discontinuities. In combination with a smoothed contact force law and the employed C1-continuous beam elements, this procedure drastically reduces the numerical integration error, an essential prerequisite for optimal spatial convergence rates. The resulting line-to-line contact algorithm is supplemented by contact contributions of the beam endpoints, which represent boundary minima of the underlying minimal distance problem. Finally, a series of numerical test cases is analyzed in order to investigate the accuracy and consistency of the proposed formulation regarding integration error, spatial convergence behavior and resulting contact force distributions.

cs.CE↗

arXiv1999

Analysis of a three flavor neutrino oscillation fit to recent Super-Kamiokande data

We have analyzed the most recent available Super-Kamiokande data in a three flavor neutrino oscillation model. We have here neglected possible matter effects and performed a fit to atmospheric and solar Super-Kamiokande data. We have investigated a large parameter range, where the mixing angles were restricted to $0 \leq θ_i \leq π/2$, $ i=1,2,3$, and the mass squared differences were taken to be in the intervals $10^{-11} {\rm eV}^2 \leq Δm^2 \leq 10^{-2} {\rm eV}^2$ and $10^{-4} {\rm eV}^2 \leq ΔM^2 \leq 10 {\rm eV}^2$. This yielded a best solution characterized by the parameter values $θ_1 \simeq 45^\circ$, $θ_2 \simeq 10^\circ$, $θ_3 \simeq 45^\circ$, $Δm^2 \simeq 4.4 \times 10^{-10} {\rm eV}^2$, and $ΔM^2 \simeq 1.01 \times 10^{-3} {\rm eV}^2$, which shows that the analyzed experimental data speak in favor of a bimaximal mixing scenario with one of the mass squared differences in the ``just-so'' domain and the other one in the range capable of providing a solution to the atmospheric neutrino problem.

hep-ph↗