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Christoph Meier

Publications and source records attributed to Christoph Meier.

At least 19 recordsLinked to original sources
arXiv2026

A hybrid sharp-diffuse interface approach to accurately model melt pool dynamics with rapid evaporation in laser-based processing of metals

Predictive simulation of melt pool dynamics in laser-based processing of metals, e.g., laser beam welding or laser powder bed fusion additive manufacturing, requires accurate resolution of thermo-hydrodynamic interactions at the melt-gas interface. Here, evaporation-induced recoil pressure and temperature-dependent surface tension govern the flow. Because these mechanisms depend sensitively, often exponentially, on the interface temperature, reliable predictions demand highly accurate heat transfer models. Popular diffuse-interface formulations smear the extreme thermal gradients as typical for laser-metal interactions, leading to interface temperature errors that critically degrade the accuracy of interface force predictions and melt pool dynamics. We present a hybrid sharp-diffuse interface approach for high-fidelity modelling of melt pool thermo-hydrodynamics with rapid evaporation. The heat transfer problem is represented using a sharp-interface unfitted finite element (CutFEM) formulation, enabling accurate prediction of the temperature field. The multi-phase flow problem, characterized by large density ratios and complex interface dynamics, is accurately captured using a robust level-set-based one-fluid diffuse-interface finite element formulation. Consistent coupling is achieved by extending the sharp-interface temperature into a narrow interface region to evaluate temperature-dependent interface forces within the diffuse-interface flow framework. In practically relevant benchmarks, the sharp-interface thermal model exhibits second-order spatial convergence, enabling finite element sizes two orders of magnitude larger than the diffuse-interface approach for 1 accuracy. In a novel coupled thermo-hydrodynamic benchmark representative of laser-metal interactions, the hybrid approach is one order of magnitude more accurate than a purely diffuse-interface model on the same mesh. Robu

cs.CE↗
arXiv2026

A variationally consistent beam-to-beam point coupling formulation for geometrically exact beam theories

Slender beam-like structures frequently occur in engineering applications and often interact at discrete locations through joints or connectors. Accurate modeling of such interactions is particularly challenging when different numerical formulations are involved in terms of underlying beam theory, interpolation schemes, and rotation parametrization. In this work, a versatile formulation-independent beam-to-beam point coupling approach is proposed within the framework of the geometrically exact beam theory discretized by the finite element method. The coupling constraints are expressed solely in terms of cross-section kinematics, namely centroid positions and orientations. Suitable generalized deformation measures for positional and rotational coupling are introduced, allowing for general coupling configurations, including relative rotations and non-coincident cross-section centroids in the reference configuration. The contribution of the coupling conditions to the weak form of the balance equations is derived in a variationally consistent manner and can be incorporated directly into the weak form of existing beam finite element models. Constraint enforcement is formulated using a Lagrange multiplier method and a penalty regularization. The proposed approach satisfies key properties such as objectivity, symmetry, and consistency with an stress-free reference configuration. Numerical examples demonstrate the robustness and flexibility of the method for coupling beams with different formulations and discretizations, even when the interaction points are located at arbitrary positions within beam elements.

cs.CE↗
arXiv2025

Spreading of highly cohesive metal powders with transverse oscillation kinematics

Powder bed additive manufacturing processes such as laser powder bed fusion (LPBF) or binder jetting (BJ) benefit from using fine (D50 $\leq20~\mu m$) powders. However, the increasing level of cohesion with decreasing particle size makes spreading a uniform and continuous layer challenging. As a result, LPBF typically employs a coarser size distribution, and rotating roller mechanisms are used in BJ machines, that can create wave-like surface profiles due to roller run-out. In this work, a transverse oscillation kinematic for powder spreading is proposed, explored computationally, and validated experimentally. Simulations are performed using an integrated discrete element-finite element (DEM-FEM) framework and predict that transverse oscillation of a non-rotating roller facilitates the spreading of dense powder layers (beyond 50% packing fraction) with a high level of robustness to kinematic parameters. The experimental study utilizes a custom-built mechanized powder spreading testbed and X-ray transmission imaging for the analysis of spread powder layers. Experimental results generally validate the computational results, however, also exhibit parasitic layer cracking. For transverse oscillation frequencies above 200 Hz, powder layers of high packing fraction (between 50-60%) were formed, and for increased layer thicknesses, highly uniform and continuous layers were deposited. Statistical analysis of the experimental powder layer morphology as a function of kinematic spreading parameters revealed that an increasing transverse surface velocity improves layer uniformity and reduces cracking defects. This suggests that with minor improvements to the machine design, the proposed transverse oscillation kinematic has the potential to result in thin and consistently uniform powder layers of highly cohesive powder.

physics.app-ph↗
arXiv2025

TEDDY: A Family Of Foundation Models For Understanding Single Cell Biology

Understanding the biological mechanisms of disease is crucial for medicine, and in particular, for drug discovery. AI-powered analysis of genome-scale biological data holds great potential in this regard. The increasing availability of single-cell RNA sequencing data has enabled the development of large foundation models for disease biology. However, existing foundation models only modestly improve over task-specific models in downstream applications. Here, we explored two avenues for improving single-cell foundation models. First, we scaled the pre-training data to a diverse collection of 116 million cells, which is larger than those used by previous models. Second, we leveraged the availability of large-scale biological annotations as a form of supervision during pre-training. We trained the \model family of models comprising six transformer-based state-of-the-art single-cell foundation models with 70 million, 160 million, and 400 million parameters. We vetted our models on several downstream evaluation tasks, including identifying the underlying disease state of held-out donors not seen during training, distinguishing between diseased and healthy cells for disease conditions and donors not seen during training, and probing the learned representations for known biology. Our models showed substantial improvement over existing works, and scaling experiments showed that performance improved predictably with both data volume and parameter count.

cs.LG↗
arXiv2025

A consistent diffuse-interface finite element approach to rapid melt--vapor dynamics with application to metal additive manufacturing

Metal additive manufacturing via laser-based powder bed fusion (PBF-LB/M) faces performance-critical challenges due to complex melt pool and vapor dynamics, often oversimplified by computational models that neglect crucial aspects, such as vapor jet formation. To address this limitation, we propose a consistent computational multi-physics mesoscale model to study melt pool dynamics, laser-induced evaporation, and vapor flow. In addition to the evaporation-induced pressure jump, we also resolve the evaporation-induced volume expansion and the resulting velocity jump at the liquid--vapor interface. We use an anisothermal incompressible Navier--Stokes solver extended by a conservative diffuse level-set framework and integrate it into a matrix-free adaptive finite element framework. To ensure accurate physical solutions despite extreme density, pressure and velocity gradients across the diffuse liquid--vapor interface, we employ consistent interface source term formulations developed in our previous work. These formulations consider projection operations to extend solution variables from the sharp liquid--vapor interface into the computational domain. Benchmark examples, including film boiling, confirm the accuracy and versatility of the model. As a key result, we demonstrate the model's ability to capture the strong coupling between melt and vapor flow dynamics in PBF-LB/M based on simulations of stationary laser illumination on a metal plate. Additionally, we show the derivation of the well-known Anisimov model and extend it to a new hybrid model. This hybrid model, together with consistent interface source term formulations, especially for the level-set transport velocity, enables PBF-LB/M simulations that combine accurate physical results with the robustness of an incompressible, diffuse-interface computational modeling framework.

cs.CE↗
arXiv2024

Patient-specific coronary angioplasty simulations -- a mixed-dimensional finite element modeling approach

Coronary angioplasty with stent implantation is the most frequently used interventional treatment for coronary artery disease. However, reocclusion within the stent, referred to as in-stent restenosis, occurs in up to 10% of lesions. It is widely accepted that mechanical loads on the vessel wall strongly affect adaptive and maladaptive mechanisms. Yet, the role of procedural and lesion-specific influence on restenosis risk remains understudied. Computational modeling of the stenting procedure can provide new mechanistic insights, such as local stresses, that play a significant role in tissue growth and remodeling. Previous simulation studies often featured simplified artery and stent geometries and cannot be applied to real-world examples. Realistic simulations were computationally expensive since they featured fully resolved stenting device models. The aim of this work is to develop and present a mixed-dimensional formulation to simulate the patient-specific stenting procedure with a reduced-dimensional beam model for the stent and 3D models for the artery. In addition to presenting the numerical approach, we apply it to realistic cases to study the intervention's mechanical effect on the artery and correlate the findings with potential high-risk locations for in-stent restenosis. We found that high artery wall stresses develop during the coronary intervention in severely stenosed areas and at the stent boundaries. Herewith, we lay the groundwork for further studies towards preventing in-stent restenosis after coronary angioplasty.

cs.CE↗
arXiv2024

A highly efficient computational approach for part-scale microstructure predictions in Ti-6Al-4V additive manufacturing

Fast and efficient simulations of metal additive manufacturing (AM) processes are highly relevant to exploring the full potential of this promising manufacturing technique. The microstructure composition plays an important role in characterizing the part quality and deriving mechanical properties. When complete parts are simulated, one often needs to resort to strong simplifications such as layer-wise heating due to the large number of simulated time steps compared to the small time step sizes. This article proposes a scan-resolved approach to the coupled thermo-microstructural problem. Building on a highly efficient thermal model, we discuss the implementation of a phenomenological microstructure model for the evolution of the three main constituents of Ti-6Al-4V: stable $\alpha_s$-phase, martensite $\alpha_m$-phase and $\beta$-phase. The implementation is tailored to modern hardware features using vectorization and fast approximations of transcendental functions. A performance model and numerical examples verify the high degree of optimization. We demonstrate the applicability and predictive power of the approach and the influence of scan strategy and geometry. Depending on the specific example, results can be obtained with moderate computational resources in a few hours to days. The numerical examples include a prediction of the microstructure on the full NIST AM Benchmark cantilever specimen.

cs.CE↗
arXiv2024

Improved accuracy of continuum surface flux models for metal additive manufacturing melt pool simulations

Computational modeling of the melt pool dynamics in laser-based powder bed fusion metal additive manufacturing (PBF-LB/M) promises to shed light on fundamental mechanisms of defect generation. These processes are accompanied by rapid evaporation so that the evaporation-induced recoil pressure and cooling arise as major driving forces for fluid dynamics and temperature evolution. The magnitude of these interface fluxes depends exponentially on the melt pool surface temperature, which, therefore, has to be predicted with high accuracy. The present work utilizes a diffuse interface finite element model based on a continuum surface flux (CSF) description of interface fluxes to study dimensionally reduced thermal two-phase problems representative for PBF-LB/M in a finite element framework. It is demonstrated that the extreme temperature gradients combined with the high ratios of material properties between metal and ambient gas lead to significant errors in the interface temperatures and fluxes when classical CSF approaches, along with typical interface thicknesses and discretizations, are applied. It is expected that this finding is also relevant for other types of diffuse interface PBF-LB/M melt pool models. A novel parameter-scaled CSF approach is proposed, which is constructed to yield a smoother temperature field in the diffuse interface region, significantly increasing the solution accuracy. The interface thickness required to predict the temperature field with a given level of accuracy is less restrictive by at least one order of magnitude for the proposed parameter-scaled approach compared to classical CSF, drastically reducing computational costs. Finally, we showcase the general applicability of the parameter-scaled CSF to a 3D simulation of stationary laser melting of PBF-LB/M considering the fully coupled thermo-hydrodynamic multi-phase problem, including phase change.

cs.CE↗
arXiv2024

A consistent diffuse-interface model for two-phase flow problems with rapid evaporation

We present accurate and mathematically consistent formulations of a diffuse-interface model for two-phase flow problems involving rapid evaporation. The model addresses challenges including discontinuities in the density field by several orders of magnitude, leading to high velocity and pressure jumps across the liquid-vapor interface, along with dynamically changing interface topologies. To this end, we integrate an incompressible Navier-Stokes solver combined with a conservative level-set formulation and a regularized, i.e., diffuse, representation of discontinuities into a matrix-free adaptive finite element framework. The achievements are three-fold: First, we propose mathematically consistent definitions for the level-set transport velocity in the diffuse interface region by extrapolating the velocity from the liquid or gas phase. They exhibit superior prediction accuracy for the evaporated mass and the resulting interface dynamics compared to a local velocity evaluation, especially for strongly curved interfaces. Second, we show that accurate prediction of the evaporation-induced pressure jump requires a consistent, namely a reciprocal, density interpolation across the interface, which satisfies local mass conservation. Third, the combination of diffuse interface models for evaporation with standard Stokes-type constitutive relations for viscous flows leads to significant pressure artifacts in the diffuse interface region. To mitigate these, we propose to introduce a correction term for such constitutive model types. Through selected analytical and numerical examples, the aforementioned properties are validated. The presented model promises new insights in simulation-based prediction of melt-vapor interactions in thermal multiphase flows such as in laser-based powder bed fusion of metals.

cs.CE↗
arXiv2023

A novel mesh regularization approach based on finite element distortion potentials: Application to material expansion processes with extreme volume change

The accuracy of finite element solutions is closely tied to the mesh quality. In particular, geometrically nonlinear problems involving large and strongly localized deformations often result in prohibitively large element distortions. In this work, we propose a novel mesh regularization approach allowing to restore a non-distorted high-quality mesh in an adaptive manner without the need for expensive re-meshing procedures. The core idea of this approach lies in the definition of a finite element distortion potential considering contributions from different distortion modes such as skewness and aspect ratio of the elements. The regularized mesh is found by minimization of this potential. Moreover, based on the concept of spatial localization functions, the method allows to specify tailored requirements on mesh resolution and quality for regions with strongly localized mechanical deformation and mesh distortion. In addition, while existing mesh regularization schemes often keep the boundary nodes of the discretization fixed, we propose a mesh-sliding algorithm based on variationally consistent mortar methods allowing for an unrestricted tangential motion of nodes along the problem boundary. Especially for problems involving significant surface deformation (e.g., frictional contact), this approach allows for an improved mesh relaxation as compared to schemes with fixed boundary nodes. To transfer data such as tensor-valued history variables of the material model from the old (distorted) to the new (regularized) mesh, a structure-preserving invariant interpolation scheme for second-order tensors is employed, which has been proposed in our previous work and is designed to preserve important mechanical properties of tensor-valued data such as objectivity and positive definiteness... {continued see pdf}

cs.CE↗
arXiv2023

Exploration of improved, roller-based spreading strategies for cohesive powders in additive manufacturing via coupled DEM-FEM simulations

Spreading of fine (D50 <=20um) powders into thin layers typically requires a mechanism such as a roller to overcome the cohesive forces between particles. Roller-based spreading requires careful optimization and can result in low density and/or inconsistent layers depending on the characteristics of the powder feedstock. Here, we explore improved, roller-based spreading strategies for highly cohesive powders using an integrated discrete element-finite element (DEM-FEM) framework. Powder characteristics are emulated using a self-similarity approach based on experimental calibration for a Ti-6Al-4V 0-20um powder. We find that optimal roller-based spreading relies on a combination of surface friction of the roller and roller kinematics that impart sufficient kinetic energy to break cohesive bonds between powder particles. However, excess rotation can impart excessive kinetic energy, causing ejection of particles and a non-uniform layer. Interestingly, the identified optimal surface velocities for counter-rotation as well as rotational oscillation are very similar, suggesting this quantity as the critical kinematic parameter. When these conditions are chosen appropriately, layers with packing fractions beyond 50% are predicted for layer thicknesses as small as ~2 times D90 of the exemplary powder, and the layer quality is robust with respect to substrate adhesion over a 10-fold range. The latter is an important consideration given the spatially varying substrate conditions in AM due to the combination of fused/bound and bare powder regions. As compared to counter-rotation, the proposed rotational oscillation is particularly attractive because it can overcome practical issues with mechanical runout of roller mechanisms. In particular, the application to rubber-coated rollers, which promises to reduce the risk of tool damage and particle streaking, is recommended for future investigation.

cs.CE↗
arXiv2023

Towards Additively Manufactured Metamaterials with Powder Inclusions for Controllable Dissipation: The Critical Influence of Packing Density

Particle dampers represent a simple yet effective means to reduce unwanted oscillations when attached to structural components. Powder bed fusion additive manufacturing of metals allows to integrate particle inclusions of arbitrary shape, size and spatial distribution directly into bulk material, giving rise to novel metamaterials with controllable dissipation without the need for additional external damping devices. At present, however, it is not well understood how the degree of dissipation is influenced by the properties of the enclosed powder packing. In the present work, a two-way coupled discrete element - finite element model is proposed allowing for the first time to consistently describe the interaction between oscillating deformable structures and enclosed powder packings. As fundamental test case, the free oscillations of a hollow cantilever beam filled with various powder packings differing in packing density, particle size, and surface properties are considered to systematically study these factors of influence. Critically, it is found that the damping characteristics strongly depend on the packing density of the enclosed powder and that an optimal packing density exists at which the dissipation is maximized. Moreover, it is found that the influence of (absolute) particle size on dissipation is rather small. First-order analytical models for different deformation modes of such powder cavities are derived to shed light on this observation.

cs.CE↗
arXiv2023

A highly efficient computational framework for fast scan-resolved simulations of metal additive manufacturing processes on the scale of real parts

This article proposes a novel high-performance computing approach for the prediction of the temperature field in powder bed fusion (PBF) additive manufacturing processes. In contrast to many existing approaches to part-scale simulations, the underlying computational model consistently resolves physical scan tracks without additional heat source scaling, agglomeration strategies or any other heuristic modeling assumptions. A growing, adaptively refined mesh accurately captures all details of the laser beam motion. Critically, the fine spatial resolution required for resolved scan tracks in combination with the high scan velocities underlying these processes mandates the use of comparatively small time steps to resolve the underlying physics. Explicit time integration schemes are well-suited for this setting, while unconditionally stable implicit time integration schemes are employed for the interlayer cool down phase governed by significantly larger time scales. These two schemes are combined and implemented in an efficient fast operator evaluation framework providing significant performance gains and optimization opportunities. The capabilities of the novel framework are demonstrated through realistic AM examples on the centimeter scale including the first scan-resolved simulation of the entire NIST AM Benchmark cantilever specimen, with a computation time of less than one day. Apart from physical insights gained through these simulation examples, also numerical aspects are thoroughly studied on basis of weak and strong parallel scaling tests. As potential applications, the proposed thermal PBF simulation framework can serve as a basis for microstructure and thermo-mechanical predictions on the part-scale, but also to assess the influence of scan pattern and part geometry on melt pool shape and temperature, which are important indicators for well-known process instabilities.

cs.CE↗
arXiv2022

Structure-Preserving Invariant Interpolation Schemes for Invertible Second-Order Tensors

Tensor interpolation is an essential step for tensor data analysis in various fields of application and scientific disciplines. In the present work, novel interpolation schemes for general, i.e., symmetric or non-symmetric, invertible square tensors are proposed. Critically, the proposed schemes rely on a combined polar and spectral decomposition of the tensor data $\boldsymbol{T}\!\!=\!\!\boldsymbol{R}\boldsymbol{Q}^T \!\! \boldsymbolΛ \boldsymbol{Q}$, followed by an individual interpolation of the two rotation tensors $\boldsymbol{R}$ and $\boldsymbol{Q}$ and the positive definite diagonal eigenvalue tensor $\boldsymbolΛ$ resulting from this decomposition. Two different schemes are considered for a consistent rotation interpolation within the special orthogonal group $\mathbb{SO}(3)$, either based on relative rotation vectors or quaternions. For eigenvalue interpolation, three different schemes, either based on the logarithmic weighted average, moving least squares or logarithmic moving least squares, are considered. It is demonstrated that the proposed interpolation procedure preserves the structure of a tensor, i.e., $\boldsymbol{R}$ and $\boldsymbol{Q}$ remain orthogonal tensors and $\boldsymbolΛ$ remains a positive definite diagonal tensor during interpolation, as well as scaling and rotational invariance (objectivity). Based on selected numerical examples considering the interpolation of either symmetric or non-symmetric tensors, the proposed schemes are compared to existing approaches such as Euclidean, Log-Euclidean, Cholesky and Log-Cholesky interpolation. In contrast to these existing methods, the proposed interpolation schemes result in smooth and monotonic evolutions of tensor invariants such as determinant, trace, fractional anisotropy (FA), and Hilbert's anisotropy (HA)...{continued see pdf}

cs.CE↗
arXiv2022

A consistent mixed-dimensional coupling approach for 1D Cosserat beams and 2D surfaces in 3D space

The present article proposes a novel computational method for coupling arbitrarily curved 1D fibers with a 2D surface as defined, e.g., by the 2D surfaces of a 3D solid body or by 2D shell formulations. The fibers are modeled as 1D Cosserat continua (beams) with six local degrees of freedom, three positional and three rotational ones. A kinematically consistent 1D-2D coupling scheme for this problem type is proposed considering the positional and rotational degrees of freedom along the beams. The positional degrees of freedom are coupled by enforcing a constant normal distance between a point on the beam centerline and a corresponding point on the surface. This strategy requires a consistent description of the surface normal vector field to guarantee fundamental mechanical properties such as conservation of angular momentum. Coupling of the rotational degrees of freedom of the beams and a suitable rotation tensor representing the local orientation within a solid volume has been considered in a previous contribution. In the present work, this coupling approach will be extended by constructing rotation tensors that are representative of local surface orientations. Several numerical examples demonstrate the consistency, robustness and accuracy of the proposed method. To showcase its applicability to multi-physics systems of practical relevance, the fluid-structure interaction example of a vascular stent is presented.

cs.CE↗
arXiv2022

Quantitative analysis of thin metal powder layers via transmission X-ray imaging and discrete element simulation: Roller-based spreading approaches

A variety of tools can be used for spreading metal, ceramic, and polymer feedstocks in powder bed additive manufacturing methods. Rollers are often employed when spreading powders with limited flowability, as arises in powders comprising fine particle sizes or high surface energy materials. Here, we study roller-based powder spreading for powder bed AM using the unique combination of a purpose-built powder spreading testbed with a proven method for X-ray mapping of powder layer depth. We focus on the density and uniformity of nominally 100 micrometer thick layers of roller-spread Ti-6Al-4V and Al-10Si-Mg powders. Our results indicate that when rotation is too rapid, roller-applied shear force impedes the creation of dense and uniform layers from powders of high innate flowability, or where inertial forces driven by particle density dominate cohesive forces. Roller counter-rotation augments the uniformity of cohesive powder layers, primarily though reducing the influence of particle clusters in the flowing powder, which are otherwise shown to cause deep, trench-like streaks. Companion discrete element method (DEM) simulations further contextualize the experiments through isolation of the effects of cohesion on layer attributes. Results suggest that roller motion parameters could apply a strategic level of additional shear force to the flowing powder, thereby mitigating the clumping behavior characteristic of highly cohesive feedstocks while maintaining high layer uniformity.

physics.app-ph↗
arXiv2022

Quantitative analysis of thin metal powder layers via transmission X-ray imaging and discrete element simulation: Blade-based spreading approaches

Spreading uniform and dense layers is of paramount importance to creating high-quality components using powder bed additive manufacturing (AM). Blade-like tools are often employed for spreading powder metal feedstocks, especially in laser powder bed fusion and electron beam melting, where powders are characterized by a D50 of 30 microns or greater. Along with variations in boundary conditions introduced by the layer-wise geometry and surface topography of the printed component, stochastic interactions between the spreading tool and powder result in spatial variations of layer quality that are still not well understood. Here, to study powder spreading under conditions representative of powder bed AM, we employ a modular, mechanized apparatus to create powder layers from moderately and highly cohesive powders with a selection of blade-like spreading tools. Powder layer effective depth is spatially mapped using transmission X-ray imaging, and uniformity is quantified via a statistical approach. We first compare layer density, or the effective depth of powder layer, and show that blade geometries with a curved profile lead to increased material deposition. Second, this approach enables quantification of local fluctuations, or layer defect severity. For example, we observe that the primary benefit of a V-shaped rubber blade, as compared to a 45 degree rigid blade, lies in enabling local deflection of the blade edge to eliminate streaking from large particles, while also increasing deposition. Additionally, we employ a custom DEM simulation to elucidate the opposing roles of particle density and surface energy with a pseudo-material approach, where the balance of inertial and cohesive forces determine macro-scale powder flowability. For specific alloy densities, we find a critical surface energy beyond which layer density is greatly impaired when powder spreading is performed using a blade.

physics.app-ph↗