arXiv subjects

Ingo Steinbach

Publications and source records attributed to Ingo Steinbach.

15 recordsLinked to original sources

arXiv2026

Phase field as a front propagation method for modeling grain growth in additive manufacturing

A mesoscopic grain-envelope model applying a phase-field front-propagation method is developed to simulate grain growth under additive manufacturing process conditions. The envelope represents the outer surface of dendritic grains through a diffuse interface. While a modified heat-conduction model that incorporates moving heat sources and latent-heat release provides the evolution of local thermal field. Envelope propagation is determined from microscopic-solvability-based kinetic law. The model is validated through two- and three-dimensional simulations and subsequently applied to examine the influence of material and process parameters on microstructure evolution. The results demonstrate that the proposed mesoscopic model offers an efficient and predictive approach for modeling grain growth during multi-pass and multi-layer build-up in additive manufacturing.

cond-mat.mtrl-sci↗

arXiv2023

Concept of introverted space: is extroverted, multidimensional space an illusion?

The quantum-phase-field concept of matter is revisited with special emphasis on the introverted view of space. Extroverted space surrounds physical objects, while introverted space lies in between physical objects. Space between objects leads to a network structure of matter: a network in which one-dimensional space filaments connect massive elementary particles. Missing quantum fluctuations in the finite space filaments are interpreted as `gravitons,' the exchange particles of gravitational attraction between elementary particles.

physics.gen-ph↗

arXiv2023

Multi-phase-field elasticity model based on partial rank-one energy relaxation on pairwise interfaces

To model mechanically-driven phase transformations using the phase-field theory, suitable models are needed for describing the mechanical fields related to individual phase-fields in the interfacial regions. They play a crucial role in obtaining the mechanical driving forces of phase-field evolution. Quantitative modeling requires satisfying the interfacial static equilibrium and kinematic compatibility conditions. To the best of our knowledge, no existing multi-phase-field elasticity model has been able to satisfy the jump conditions between all the locally-active phase-fields associated to their pairwise normals, except in the dual-phase-field regions. In this work, we introduce a novel multi-phase-field elasticity model based on the partial rank-one relaxation of the elastic energy density defined on the pairwise interfaces as a function of pairwise strains. These ad hoc pairwise definitions enable us to satisfy the static equilibrium and kinematic compatibility conditions between all the locally-active phase-fields. Different numerical examples are presented, which compare the developed model against the equal-strain and equal-stress limiting cases.

math.NA↗

arXiv2020

Multi-phase-field modeling of microstructure evolution in metallic foams

This paper represents a model for microstructure formation in metallic foams based on the multi-phase-field (MPF) approach. By the use of a no-coalescence boundary condition within this MPF-framework, it is possible to completely prevent coalescence of bubbles and thus focus on the formation of a closed porous microstructure. A modification of this non-wetting criterion allows for the controlled initiation of coalescence and the evolution of open structures. The method is validated and used to simulate foam structure formation both in two and three dimensions.

physics.comp-ph↗

arXiv2020

Self similarity of the expanding universe as understood by quantum-phase-fields

An idea of the universe as a self-contained system of interacting fields as a closed doublon network is developed. The characteristic scale of this system is considered emergent from general principles. Self similarity of patterns in the universe can be understood by introducing a characteristic scale with respect towhich patterns are evaluated. The developed physical-mathematical model is in good agreement with cosmological length scales and gives a rationale of the empirical fact for an expanding universe. Within the framework of the de~Broglie-Bohm double solution program, the model can be applied to rationalize the existence of a ground potential and a cosmological constant.

physics.gen-ph↗

arXiv2019

Quantum-phase-field: from de Broglie--Bohm double solution program to doublon networks

We study different forms of linear and non-linear field equations, so-called `phase-field' equations, in relation to the de~Broglie-Bohm double solution program. This defines a framework in which elementary particles are described by localized non-linear wave solutions moving by the guidance of a pilot wave, defined by the solution of a Schrödinger type equation. First, we consider the phase-field order parameter as the phase for the linear pilot wave, second as the pilot wave itself and third as a moving soliton interpreted as a massive particle. In the last case, we introduce the equation for a superwave, the amplitude of which can be considered as a particle moving in accordance to the de~Broglie-Bohm theory. Lax pairs for the coupled problems are constructed in order to discover possible non-linear equations which can describe the moving particle and to propose a framework for investigating coupled solutions. Finally, doublons in 1+1 dimensions are constructed as self similar solutions of a non-linear phase-field equation forming a finite space-object. Vacuum quantum oscillations within the doublon determine the evolution of the coupled system. Applying a conservation constraint and using general symmetry considerations, the doublons are arranged as a network in 1+1+2 dimensions where nodes are interpreted as elementary particles. A canonical procedure is proposed to treat charge and electromagnetic exchange.

physics.gen-ph↗

arXiv2019

Controlling bubble coalescence in metallic foams: A simple phase field-based approach

The phase-field method is used as a basis to develop a strictly mass conserving, yet simple, model for simulation of two-phase flow. The model is aimed to be applied for the study of structure evolution in metallic foams. In this regard, the critical issue is to control the rate of bubble coalescence compared to concurrent processes such as their rearrangement due to fluid motion. In the present model, this is achieved by tuning the interface energy as a free parameter. The model is validated by a number of benchmark tests. First, stability of a two dimensional bubble is investigated by the Young-Laplace law for different values of the interface energy. Then, the coalescence of two bubbles is simulated until the system reaches equilibrium with a circular shape. To address the major capability of the present model for the formation of foam structure, the bubble coalescence is simulated for various values of interface energy in order to slow down the merging process. These simulations are repeated in the presence of a rotational flow to highlight the fact that the model allows to suppress the coalescence process compared to the motion of bubbles relative to each other.

physics.comp-ph↗

arXiv2019

Thin interface limit for phase-field models of solidification with local mobility correction

A new approach is developed to derive an analytical form for mobility corrections in phase-field models for pure material solidification. Similar to the thin interface limit approach (Karma and Rappel, 1996) it seeks to remove systematic errors in the kinetics of phase-field models that arise due to the diffusivity of the interface. The new approach harnesses local information within the diffuse interface instead of an expansion within the interface peclet number $p_e=η/δ$, the ratio of diffuse interface thickness to diffusion length. Therefore it has no need for an approximation of $p_e$ being small. This results in a broader range of applicability of the approach for higher $p_e$.

physics.comp-ph↗

arXiv2018

Concentration-dependent atomic mobilities in FCC CoCrFeMnNi high-entropy alloys

The diffusion kinetics in a CoCrFeMnNi high entropy alloy is investigated by a combined radiotracer--interdiffusion experiment applied to a pseudo-binary Co$_{15}$Cr$_{20}$Fe$_{20}$Mn$_{20}$Ni$_{25}$ / Co$_{25}$Cr$_{20}$Fe$_{20}$Mn$_{20}$Ni$_{15}$ couple. As a result, the composition-dependent tracer diffusion coefficients of Co, Cr, Fe and Mn are determined. The elements are characterized by significantly different diffusion rates, with Mn being the fastest element and Co being the slowest one. The elements having originally equiatomic concentration through the diffusion couple are found to reveal up-hill diffusion, especially Cr and Mn. The atomic mobility of Co seems to follow an S-shaped concentration dependence along the diffusion path. The experimentally measured kinetic data are checked against the existing CALPHAD-type databases. In order to ensure a consistent treatment of tracer and chemical diffusion a generalized symmetrized continuum approach for multi-component interdiffusion is proposed. Both, tracer and chemical diffusion concentration profiles are simulated and compared to the measurements. By using the measured tracer diffusion coefficients the chemical profiles can be described, almost perfectly, including up-hill diffusion.

cond-mat.mtrl-sci↗

arXiv2017

Computationally efficient phase-field studies combining simulation sampling and statistical analysis

The trade-off between accuracy and computational cost as a function of the size and number of simulation boxes was studied for large-scale phase-field simulations. For this purpose, a reference simulation box was incrementally partitioned. We have considered diffusion-controlled precipitation of delta prime in a model Al-Li system from the growth stage until early ripening. The results of the simulations show that decomposition of simulation box can be a valuable computational technique to accelerate simulations without substantial loss of accuracy. In the current case study, the precipitate density was found to be the key controlling parameter. For a pre-set accuracy, it turned out that large-scale simulations of the reference domain can be replaced by a combination of smaller simulations. This shortens the required simulation time and improves the memory usage of the simulation considerably, and thus substantially increases the efficiency of massive parallel computation for phase-field applications.

cond-mat.mtrl-sci↗

arXiv2017

A multi-phase-field method for surface tension-induced elasticity

A consistent treatment of the coupling of surface energy and elasticity within the multi-phase- field framework is presented. The model accurately reproduces stress distribution in a number of analytically tractable, yet non-trivial, cases including different types of spherical heterogeneities and a thin plate suspending in a gas environment. It is then used to study the stress distribution inside elastic bodies with non-spherical geometries, such as a solid ellipsoid and a sintered structure. In these latter cases, it is shown that the interplay between deformation and spatially variable surface curvature leads to heterogeneous stress distribution across the specimen.

cond-mat.mes-hall↗

arXiv2017

Multi-Phase-Field Model for Surface/Phase-Boundary Diffusion

The multi-phase-field approach is generalized to treat capillarity-driven diffusion parallel to the surfaces and phase-boundaries, i.e. the boundaries between a condensed phase and its vapor and the boundaries between two or multiple condensed phases. The effect of capillarity is modeled via curvature-dependence of the chemical potential whose gradient gives rise to diffusion. The model is used to study thermal grooving on the surface of a polycrystalline body. Decaying oscillations of the surface profile during thermal grooving, postulated by Hillert long ago but reported only in few studies so far, are observed and discussed. Furthermore, annealing of multi-nano-clusters on a deformable free surface is investigated using the proposed model. Results of these simulations suggest that the characteristic crater-like structure with an elevated perimeter, observed in recent experiments, is a transient non-equilibrium state during the annealing process.

cond-mat.mes-hall↗

arXiv2017

Quantum-phase-field concept of matter: Emergent gravity in the dynamic universe

A monistic framework is set up where energy is the only fundamental substance. Different states of energy are ordered by a set of scalar qunatum-phase-fields. The dual elements of matter, mass and space, are described as volume- and gradient-energy contributions of the set of fields, respectively. Time and space are formulated as background-independent dynamic variables. The evolution equations of the body of the universe are derived from first principles of thermodynamics. Gravitational interaction emerges from quantum fluctuations in finite space. Application to a large number of fields predicts scale separation in space and repulsive action of masses distant beyond a marginal distance. The predicted marginal distance is compared to the size of the voids in the observable universe.

physics.gen-ph↗

arXiv2011

Dynamics of cylindrical droplets on flat substrate: Lattice Boltzmann modeling versus simple analytic models

The steady state motion of cylindrical droplets under the action of external body force is investigated both theoretically and via lattice Boltzmann simulation. As long as the shape-invariance of droplet is maintained, the droplet's center-of-mass velocity linearly scales with both the force density and the square of droplet radius. However, a non-linear behavior appears as the droplet deformation becomes significant. This deformation is associated with the drop elongation occurring at sufficiently high external forcing. Yet, independent of either the force density or the droplet size, the center-of-mass velocity is found to be linear in terms of the inverse of dynamic viscosity. In addition, it is shown that the energy is mainly dissipated in a region near the substrate particularly close to the three phase contact line. The total viscous dissipation is found to be proportional to both the square of force density and the inverse of dynamic viscosity. Moreover, the dependence of the center-of-mass velocity on the equilibrium contact angle is investigated. A simple analytic model is provided reproducing the observed behavior.

cond-mat.soft↗

arXiv2009

Roughness gradient induced spontaneous motion of droplets on hydrophobic surfaces: A lattice Boltzmann study

The effect of a step wise change in the pillar density on the dynamics of droplets is investigated via three-dimensional lattice Boltzmann simulations. For the same pillar density gradient but different pillar arrangements, both motion over the gradient zone as well as complete arrest are observed. In the moving case, the droplet velocity scales approximately linearly with the texture gradient. A simple model is provided reproducing the observed linear behavior. The model also predicts a linear dependence of droplet velocity on surface tension. This prediction is clearly confirmed via our computer simulations for a wide range of surface tensions.

cond-mat.soft↗