arXiv subjects

Christoph Meier

Publications and source records attributed to Christoph Meier.

At least 37 records · Page 2Linked to original sources

arXiv2022

Analytical disk-cylinder interaction potential laws for the computational modeling of adhesive, deformable (nano)fibers

The analysis of complex fibrous systems or materials on the micro- and nanoscale, which have a high practical relevance for many technical or biological systems, requires accurate analytical descriptions of the adhesive and repulsive forces acting on the fiber surfaces. While such analytical expressions are generally needed both for theoretical studies and for computer-based simulations, the latter motivates us here to derive disk-cylinder interaction potential laws that are valid for arbitrary mutual orientations in the decisive regime of small surface separations. The chosen type of fundamental point-pair interaction follows the simple Lennard-Jones model with inverse power laws for both the adhesive van der Waals part and the steric, repulsive part. We present three different solutions, ranging from highest accuracy to the best trade-off between simplicity of the expression and sufficient accuracy for our intended use. The validity of simplifying approximations and the accuracy of the derived potential laws is thoroughly analyzed, using both numerical and analytical reference solutions for specific interaction cases. Most importantly, the correct asymptotic scaling behavior in the decisive regime of small separations is achieved, and also the theoretically predicted $(1\!/\!\sin\!α)$-angle dependence (for non-parallel cylinders) is obtained by the proposed analytical solutions. As we show in the outlook to our current research, the derived analytical disk-cylinder interaction potential laws may be used to formulate highly efficient computational models for the interaction of arbitrarily curved fibers, such that the disk represents the cross-section of the first and the cylinder a local approximation to the shape of the second fiber.

cs.CE↗

arXiv2022

Asymptotically consistent and computationally efficient modeling of short-ranged molecular interactions between curved slender fibers undergoing large 3D deformations

This article proposes a novel computational modeling approach for short-ranged molecular interactions between curved slender fibers undergoing large 3D deformations, and gives a detailed overview how it fits into the framework of existing fiber or beam interaction models, either considering microscale molecular or macroscale contact effects. The direct evaluation of a molecular interaction potential between two general bodies in 3D space would require to integrate molecule densities over two 3D volumes, leading to a sixfold integral to be solved numerically. By exploiting the short-range nature of the considered class of interaction potentials as well as the fundamental kinematic assumption of undeformable fiber cross-sections, as typically applied in mechanical beam theories, a recently derived, closed-form analytical solution is applied for the interaction potential between a given section of the first fiber (slave beam) and the entire second fiber (master beam). This novel approach based on a pre-defined section-beam interaction potential (SBIP) requires only one single integration step along the slave beam length to be performed numerically. In terms of accuracy, the total beam-beam interaction potential resulting from this approach is shown to exhibit an asymptotically consistent angular and distance scaling behavior. In addition to elementary two-fiber systems, carefully chosen to verify accuracy and asymptotic consistence of the proposed SBIP approach, a potential practical application in form of adhesive nanofiber-grafted surfaces is studied. Involving a large number of helicoidal fibers undergoing large 3D deformations, arbitrary mutual fiber orientations as well as frequent local fiber pull-off and snap-into-contact events, this example demonstrates the robustness and computational efficiency of the new approach.

cs.CE↗

arXiv2022

Generalized Section-Section Interaction Potentials in the Geometrically Exact Beam Theory: Modeling of Intermolecular Forces, Asymptotic Limit as Strain-Energy Function, and Formulation of Rotational Constraints

The present contribution proposes a universal framework to formulate generalized section-section interaction potentials (SSIP) within the geometrically exact beam theory. By exploiting the fundamental kinematic assumption of undeformable cross-sections, an objective (i.e., frame-invariant) description of SSIPs via a minimal set of six (translational and rotational) relative coordinates, either in spatial or in material form, is proposed. Based on work-pairing, work-conjugated section-section interaction forces and moments, either in spatial or in material form, are identified that can be consistently derived from a variational principle. Interestingly, it is shown that hyperelastic stored-energy functions relating the deformation measures and stress-resultants of the well-known geometrically exact Simo-Reissner beam theory can also be identified as SSIPs when considering the asymptotic limit of small relative distances and rotations between the interacting cross-sections. Moreover, the proposed variational problem formulation is demonstrated to be of a very general nature, thus allowing for the formulation of translational and rotational constraints between arbitrarily oriented cross-sections based on either a penalty or a Lagrange multiplier potential. Possible applications include fiber-based structures and materials in technical and biological systems, where the proposed approach allows to model short- or long-ranged inter-molecular (e.g., electrostatic, van der Waals or repulsive steric) interactions between fibers in geometrically complex arrangements and to formulate translational and rotational coupling constraints between different fibers (e.g., cross-linked polymer chains) or between fibers and a matrix phase (e.g., fiber-reinforced composites).

physics.class-ph↗

arXiv2022

A Versatile SPH Modeling Framework for Coupled Microfluid-Powder Dynamics in Additive Manufacturing: Binder Jetting, Material Jetting, Directed Energy Deposition and Powder Bed Fusion

Many additive manufacturing (AM) technologies rely on powder feedstock, which is fused to form the final part either by melting or by chemical binding with subsequent sintering. In both cases, process stability and resulting part quality depend on dynamic interactions between powder particles and a fluid phase, i.e., molten metal or liquid binder. The present work proposes a versatile computational modeling framework for simulating such coupled microfluid-powder dynamics problems involving thermo-capillary flow and reversible phase transitions. In particular, a liquid and a gas phase are interacting with a solid phase that consists of a substrate and mobile powder particles while simultaneously considering temperature-dependent surface tension and wetting effects. In case of laser-metal interactions, the effect of rapid evaporation is incorporated through additional mechanical and thermal interface fluxes. All phase domains are spatially discretized using smoothed particle hydrodynamics. The method's Lagrangian nature is beneficial in the context of dynamically changing interface topologies. Special care is taken in the formulation of phase transitions, which is crucial for the robustness of the computational scheme. While the underlying model equations are of a very general nature, the proposed framework is especially suitable for the mesoscale modeling of various AM processes. To this end, the generality and robustness of the computational modeling framework is demonstrated by several application-motivated examples representing the specific AM processes binder jetting, material jetting, directed energy deposition, and powder bed fusion. Among others, it is shown how the dynamic impact of droplets in binder jetting or the evaporation-induced recoil pressure in powder bed fusion leads to powder motion, distortion of the powder packing structure, and powder particle ejection.

cs.CE↗

arXiv2022

A Mortar Finite Element Formulation for Large Deformation Lubricated Contact Problems with Smooth Transition Between Mixed, Elasto-Hydrodynamic and Full Hydrodynamic Lubrication

This work proposes a novel model and numerical formulation for lubricated contact problems describing the mutual interaction between two deformable 3D solid bodies and an interposed fluid film. The solid bodies are consistently described based on nonlinear continuum mechanics allowing for finite deformations and arbitrary constitutive laws. The fluid film is modelled as a quasi-2D flow problem on the interface between the solids governed by the averaged Reynolds equation. The averaged Reynolds equation accounts for surface roughness utilizing spatially homogenized, effective fluid parameters and for cavitation through a positivity constraint imposed on the pressure field. In contrast to existing approaches, the proposed model accounts for the co-existence of frictional contact tractions and hydrodynamic fluid tractions at every local point on the contact surface of the interacting bodies and covers the entire range from boundary lubrication to mixed, elastohydrodynamic, and eventually to full film hydrodynamic lubrication in one unified modelling framework with smooth transition between these different regimes. Critically, the model relies on a recently proposed regularization scheme for the mechanical contact constraint combining the advantages of classical penalty and Lagrange multiplier approaches by expressing the mechanical contact pressure as a function of the effective gap between the solid bodies while at the same time limiting the minimal gap value occurring at the (theoretical) limit of infinitely high contact pressures. From a physical point of view, this approach can be considered as a model for the elastic deformation of surface asperities, with a bounded magnitude depending on the interacting solids' surface roughness. A consistent and accurate model behavior is demonstrated and validated by employing several challenging and practically relevant benchmark test cases.

cs.CE↗

arXiv2021

A simple yet consistent constitutive law and mortar-based layer coupling schemes for thermomechanical macroscale simulations of metal additive manufacturing processes

This article proposes a coupled thermomechanical finite element model tailored to the macroscale simulation of metal additive manufacturing processes such as selective laser melting. A first focus lies on the derivation of a consistent constitutive law on basis of a Voigt-type spatial homogenization procedure across the relevant phases, powder, melt and solid. The proposed constitutive law accounts for the irreversibility of phase change and consistently represents thermally induced residual stresses. In particular, the incorporation of a reference strain term, formulated in rate form, allows to consistently enforce a stress-free configuration for newly solidifying material at melt temperature. Application to elementary test cases demonstrates the validity of the proposed constitutive law and allows for a comparison with analytical and reference solutions. Moreover, these elementary solidification scenarios give detailed insights and foster understanding of basic mechanisms of residual stress generation in melting and solidification problems with localized, moving heat sources. As a second methodological aspect, dual mortar mesh tying strategies are proposed for the coupling of successively applied powder layers. This approach allows for very flexible mesh generation for complex geometries. As compared to collocation-type coupling schemes, e.g., based on hanging nodes, these mortar methods enforce the coupling conditions between non-matching meshes in an $L^2$-optimal manner. The combination of the proposed constitutive law and mortar mesh tying approach is validated on realistic three-dimensional examples, representing a first step towards part-scale predictions.

cs.CE↗

arXiv2021

Physics-Based Modeling and Predictive Simulation of Powder Bed Fusion Additive Manufacturing Across Length Scales

Powder bed fusion additive manufacturing (PBFAM) of metals has the potential to enable new paradigms of product design, manufacturing and supply chains while accelerating the realization of new technologies in the medical, aerospace, and other industries. Currently, wider adoption of PBFAM is held back by difficulty in part qualification, high production costs and low production rates, as extensive process tuning, post-processing, and inspection are required before a final part can be produced and deployed. Physics-based modeling and predictive simulation of PBFAM offers the potential to advance fundamental understanding of physical mechanisms that initiate process instabilities and cause defects. In turn, these insights can help link process and feedstock parameters with resulting part and material properties, thereby predicting optimal processing conditions and inspiring the development of improved processing hardware, strategies and materials. This work presents recent developments of our research team in the modeling of metal PBFAM processes spanning length scales, namely mesoscale powder modeling, mesoscale melt pool modeling, macroscale thermo-solid-mechanical modeling and microstructure modeling. Ongoing work in experimental validation of these models is also summarized. In conclusion, we discuss the interplay of these individual submodels within an integrated overall modeling approach, along with future research directions.

cs.CE↗

arXiv2021

Consistent coupling of positions and rotations for embedding 1D Cosserat beams into 3D solid volumes

This article proposes a mortar type finite element formulation for consistently embedding curved, slender beams, i.e. 1D Cosserat continua, into 3D solid volumes. A consistent 1D-3D coupling scheme for this problem type is proposed, which enforces both positional and rotational constraints. Since Boltzmann continua exhibit no inherent rotational degrees of freedom, suitable definitions of orthonormal triads are investigated that are representative for the orientation of material directions in the 3D solid. The rotation tensor defined by the polar decomposition of the deformation gradient is demonstrated to represent these material directions in a L2-optimal manner. Subsequently, objective rotational coupling constraints between beam and solid are formulated and enforced in a variationally consistent framework. Eventually, finite element discretization of all primary fields results in an embedded mortar formulation for rotational and translational constraint enforcement. Based on carefully chosen numerical test cases, the proposed scheme is demonstrated to exhibit a consistent spatial convergence behavior and to offer the up-scaling potential for studying real-life engineering applications such as fiber-reinforced composite materials.

cs.CE↗

arXiv2021

A Novel Physics-Based and Data-Supported Microstructure Model for Part-Scale Simulation of Laser Powder Bed Fusion of Ti-6Al-4V

The elasto-plastic material behavior, material strength and failure modes of metals fabricated by additive manufacturing technologies are significantly determined by the underlying process-specific microstructure evolution. In this work a novel physics-based and data-supported phenomenological microstructure model for Ti-6Al-4V is proposed that is suitable for the part-scale simulation of selective laser melting processes. The model predicts spatially homogenized phase fractions of the most relevant microstructural species, namely the stable $β$-phase, the stable $α_{\text{s}}$-phase as well as the metastable Martensite $α_{\text{m}}$-phase, in a physically consistent manner. In particular, the modeled microstructure evolution, in form of diffusion-based and non-diffusional transformations, is a pure consequence of energy and mobility competitions among the different species, without the need for heuristic transformation criteria as often applied in existing models. The mathematically consistent formulation of the evolution equations in rate form renders the model suitable for the practically relevant scenario of temperature- or time-dependent diffusion coefficients, arbitrary temperature profiles, and multiple coexisting phases. Due to its physically motivated foundation, the proposed model requires only a minimal number of free parameters, which are determined in an inverse identification process considering a broad experimental data basis in form of time-temperature transformation diagrams. Subsequently, the predictive ability of the model is demonstrated by means of continuous cooling transformation diagrams, showing that experimentally observed characteristics such as critical cooling rates emerge naturally from the proposed microstructure model, instead of being enforced as heuristic transformation criteria.

cs.CE↗

arXiv2021

A novel smoothed particle hydrodynamics and finite element coupling scheme for fluid-structure interaction: the sliding boundary particle approach

A novel numerical formulation for solving fluid-structure interaction (FSI) problems is proposed where the fluid field is spatially discretized using smoothed particle hydrodynamics (SPH) and the structural field using the finite element method (FEM). As compared to fully mesh- or grid-based FSI frameworks, due to the Lagrangian nature of SPH this framework can be easily extended to account for more complex fluids consisting of multiple phases and dynamic phase transitions. Moreover, this approach facilitates the handling of large deformations of the fluid domain respectively the fluid-structure interface without additional methodological and computational efforts. In particular, to achieve an accurate representation of interaction forces between fluid particles and structural elements also for strongly curved interface geometries, the novel sliding boundary particle approach is proposed to ensure full support of SPH particles close to the interface. The coupling of the fluid and the structural field is based on a Dirichlet-Neumann partitioned approach, where the fluid field is the Dirichlet partition with prescribed interface displacements and the structural field is the Neumann partition subject to interface forces. To overcome instabilities inherent to weakly coupled schemes an iterative fixed-point coupling scheme is employed. Several numerical examples in form of well-known benchmark tests are considered to validate the accuracy, stability, and robustness of the proposed formulation. Finally, the filling process of a highly flexible thin-walled balloon-like container is studied, representing a model problem close to potential application scenarios of the proposed scheme in the field of biomechanics.

cs.CE↗

arXiv2021

A novel smoothed particle hydrodynamics formulation for thermo-capillary phase change problems with focus on metal additive manufacturing melt pool modeling

Laser-based metal processing including welding and three dimensional printing, involves localized melting of solid or granular raw material, surface tension-driven melt flow and significant evaporation of melt due to the applied very high energy densities. The present work proposes a weakly compressible smoothed particle hydrodynamics formulation for thermo-capillary phase change problems involving solid, liquid and gaseous phases with special focus on selective laser melting, an emerging metal additive manufacturing technique. Evaporation-induced recoil pressure, temperature-dependent surface tension and wetting forces are considered as mechanical interface fluxes, while a Gaussian laser beam heat source and evaporation-induced heat losses are considered as thermal interface fluxes. A novel interface stabilization scheme is proposed, which is shown to allow for a stable and smooth liquid-gas interface by effectively damping spurious interface flows as typically occurring in continuum surface force approaches. Moreover, discretization strategies for the tangential projection of the temperature gradient, as required for the discrete Marangoni forces, are critically reviewed. The proposed formulation is deemed especially suitable for modeling of the melt pool dynamics in metal additive manufacturing because the full range of relevant interface forces is considered and the explicit resolution of the atmospheric gas phase enables a consistent description of pore formation by gas inclusion. The accuracy and robustness of the individual model and method building blocks is verified by means of several selected examples in the context of the selective laser melting process.

cs.CE↗

arXiv2021

Spatial Mapping of Powder Layer Density for Metal Additive Manufacturing via X-ray Microscopy

Uniform powder spreading is a requisite for creating consistent, high-quality components via powder bed additive manufacturing (AM), wherein layer density and uniformity are complex functions of powder characteristics, spreading kinematics, and mechanical boundary conditions. High spatial variation in particle packing density, driven by the stochastic nature of the spreading process, impedes optical interrogation of these layer attributes. Thus, we present transmission X-ray imaging as a method for directly mapping the effective depth of powder layers at process-relevant scale and resolution. Specifically, we study layers of nominal 50-250 micrometer thickness, created by spreading a selection of commercially obtained Ti-6Al-4V, 316 SS, and Al-10Si-Mg powders into precision-depth templates. We find that powder layer packing fraction may be predicted from a combination of the relative thickness of the layer as compared to mean particle size, and flowability assessed by macroscale powder angle of repose. Power spectral density analysis is introduced as a tool for quantification of defect severity as a function of morphology, and enables separate consideration of layer uniformity and sparsity. Finally, spreading is studied using multi-layer templates, providing insight into how particles interact with both previously deposited material and abrupt changes in boundary condition. Experimental results are additionally compared to a purpose-built discrete element method (DEM) powder spreading simulation framework, clarifying the competing role of adhesive and gravitational forces in layer uniformity and density, as well as particle motion within the powder bed during spreading.

physics.app-ph↗

arXiv2021

An SPH framework for fluid-solid and contact interaction problems including thermo-mechanical coupling and reversible phase transitions

The present work proposes an approach for fluid-solid and contact interaction problems including thermo-mechanical coupling and reversible phase transitions. The solid field is assumed to consist of several arbitrarily-shaped, undeformable but mobile rigid bodies, that are evolved in time individually and allowed to get into mechanical contact with each other. The fluid field generally consists of multiple liquid or gas phases. All fields are spatially discretized using the method of smoothed particle hydrodynamics (SPH). This approach is especially suitable in the context of continually changing interface topologies and dynamic phase transitions without the need for additional methodological and computational effort for interface tracking as compared to mesh- or grid-based methods. Proposing a concept for the parallelization of the computational framework, in particular concerning a computationally efficient evaluation of rigid body motion, is an essential part of this work. Finally, the accuracy and robustness of the proposed framework is demonstrated by several numerical examples in two and three dimensions, involving multiple rigid bodies, two-phase flow, and reversible phase transitions, with a focus on two potential application scenarios in the fields of engineering and biomechanics: powder bed fusion additive manufacturing (PBFAM) and disintegration of food boluses in the human stomach. The efficiency of the parallel computational framework is demonstrated by a strong scaling analysis.

cs.CE↗

arXiv2021

A Novel Modeling and Simulation Approach for the Hindered Mobility of Charged Particles in Biological Hydrogels

This article presents a novel computational model to study the selective filtering of biological hydrogels due to the surface charge and size of diffusing particles. It is the first model that includes the random 3D fiber orientation and connectivity of the biopolymer network and that accounts for elastic deformations of the fibers by means of beam theory. As a key component of the model, novel formulations are proposed both for the electrostatic and repulsive steric interactions between a spherical particle and a beam. In addition to providing a thorough validation of the model, the presented computational studies yield new insights into the underlying mechanisms of hindered particle mobility, especially regarding the influence of the aforementioned aspects that are unique to this model. It is found that the precise distribution of fiber and thus charge agglomerations in the network have a crucial influence on the mobility of oppositely charged particles and gives rise to distinct motion patterns. Considering the high practical significance for instance with respect to targeted drug release or infection defense, the provided proof of concept motivates further advances of the model toward a truly predictive computational tool that allows a case- and patient-specific assessment for real (biological) systems.

physics.bio-ph↗

arXiv2020

On phase change and latent heat models in metal additive manufacturing process simulation

This work proposes an extension of phase change and latent heat models for the simulation of metal powder bed fusion additive manufacturing processes on the macroscale and compares different models with respect to accuracy and numerical efficiency. Specifically, a systematic formulation of phase fraction variables is proposed relying either on temperature- or enthalpy-based interpolation schemes. Moreover, two well-known schemes for the numerical treatment of latent heat, namely the apparent capacity and the so-called heat integration scheme, are critically reviewed and compared with respect to numerical efficiency and overall accuracy. Eventually, a novel variant of the heat integration scheme is proposed that allows to directly control efficiency and accuracy by means of a user-defined tolerance. Depending on the chosen tolerance, it is shown that this novel approach offers increased numerical efficiency for a given level of accuracy or improved accuracy for a given level of numerical efficiency as compared to the apparent capacity and the original heat integration scheme. The investigation and comparison of all considered schemes is based on a series of numerical test cases that are representative for application scenarios in metal powder bed fusion additive manufacturing.

cs.CE↗

arXiv2019

A mortar-type finite element approach for embedding 1D beams into 3D solid volumes

In this work we present a novel computational method for embedding arbitrary curved one-dimensional (1D) fibers into three-dimensional (3D) solid volumes, as e.g. in fiber-reinforced materials. The fibers are explicitly modeled with highly efficient 1D geometrically exact beam finite elements, based on various types of geometrically nonlinear beam theories. The surrounding solid volume is modeled with 3D continuum (solid) elements. An embedded mortar-type approach is employed to enforce the kinematic coupling constraints between the beam elements and solid elements on non-matching meshes. This allows for very flexible mesh generation and simple material modeling procedures in the solid, since it can be discretized without having to capture for the reinforcements, while still being able to account for complex nonlinear effects due to the embedded fibers. Several numerical examples demonstrate the consistency, robustness and accuracy of the proposed method, as well as its applicability to rather complex fiber-reinforced structures of practical relevance.

cs.CE↗

arXiv2019

A Computational Model for Molecular Interactions Between Curved Slender Fibers Undergoing Large 3D Deformations With a Focus on Electrostatic, van der Waals and Repulsive Steric Forces

This contribution proposes the first 3D beam-to-beam interaction model for molecular interactions between curved slender fibers undergoing large deformations. While the general model is not restricted to a specific beam formulation, in the present work it is combined with the geometrically exact beam theory and discretized via the finite element method. A direct evaluation of the total interaction potential for general 3D bodies requires the integration of contributions from molecule or charge distributions over the volumes of the interaction partners, leading to a 6D integral (two nested 3D integrals) that has to be solved numerically. Here, we propose a novel strategy to formulate reduced section-to-section interaction laws for the resultant interaction potential between a pair of cross-sections of two slender fibers such that only two 1D integrals along the fibers' length directions have to be solved numerically. This section-to-section interaction potential (SSIP) approach yields a significant gain in efficiency, which is essential to enable the simulation of relevant time and length scales for many practical applications. In a first step, the generic structure of SSIP laws, which is suitable for the most general interaction scenario (e.g. fibers with arbitrary cross-section shape and inhomogeneous atomic/charge density within the cross-section) is presented. Assuming circular, homogeneous cross-sections, in a next step, specific analytical expressions for SSIP laws describing short-range volume interactions (e.g. van der Waals or steric interactions) and long-range surface interactions (e.g. Coulomb interactions) are proposed. The validity of the SSIP laws as well as the accuracy and robustness of the general SSIP approach to beam-to-beam interactions is thoroughly verified by means of a set of numerical examples considering steric repulsion, electrostatic or van der Waals adhesion.

cs.CE↗

arXiv2019

Investigation of the Peeling and Pull-off Behavior of Adhesive Elastic Fibers via a Novel Computational Beam Interaction Model

This article studies the fundamental problem of separating two adhesive elastic fibers based on numerical simulation employing a recently developed finite element model for molecular interactions between curved slender fibers. Specifically, it covers the two-sided peeling and pull-off process starting from fibers contacting along its entire length to fully separated fibers including all intermediate configurations and the well-known physical instability of snapping into contact and snapping free. We analyze the resulting force-displacement curve showing a rich and highly nonlinear system behavior arising from the interplay of adhesion, mechanical contact interaction and structural resistance against (axial, shear and bending) deformation. While similar to one-sided peeling studies from the literature, a distinct initiation and peeling phase can be observed, the two-sided peeling setup considered in the present work reveals the extended final pull-off stage as third characteristic phase. Moreover, the influence of different material and interaction parameters such as Young's modulus as well as type (electrostatic or van der Waals) and strength of adhesion is critically studied. Most importantly, it is found that the maximum force occurs in the pull-off phase for electrostatic attraction, but in the initiation phase for van der Waals adhesion. In addition to the physical system behavior, the most important numerical aspects required to simulate this challenging computational problem in a robust and accurate manner are discussed. Thus, besides the insights gained into the considered two-fiber system, this study provides a proof of concept facilitating the application of the employed model to larger and increasingly complex systems of slender fibers.

cs.CE↗