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In the manufacturing process of high-performance particulate materials, viscous sintering plays a crucial role, particularly in fields such as polymer processing and additive manufacturing. The interactions between microscopic particles,…

Computational Engineering, Finance, and Science · Computer Science 2024-12-06 Xiaoxu Dai , Bo Qian , Arkadz Kirshtein , Qingcheng Yang

We briefly review the state-of-the-art in phase-field modeling of microstructure evolution. The focus is placed on recent applications of phase-field simulations of solid-state microstructure evolution and solidification that have been…

Materials Science · Physics 2021-10-14 D. Tourret , H. Liu , J. LLorca

The resulting microstructure after the sintering process determines many materials properties of interest. In order to understand the microstructural evolution, simulations are often employed. One such simulation method is the phase-field…

Materials Science · Physics 2023-10-19 Marco Seiz , Henrik Hierl , Britta Nestler

Sintering is an important processing step in both ceramics and metals processing. The microstructure resulting from this process determines many materials properties of interest. Hence the accurate prediction of the microstructure,…

Materials Science · Physics 2024-03-06 Marco Seiz , Henrik Hierl , Britta Nestler , Wolfgang Rheinheimer

The phase-field method has become in recent years the method of choice for simulating microstructural pattern formation during solidification. One of its main advantages is that time-dependent three-dimensional simulations become feasible.…

Materials Science · Physics 2007-05-23 M. Dejmek , R. Folch , A. Parisi , M. Plapp

Sintering, as a thermal process at elevated temperature below the melting point, is widely used to bond contacting particles into engineering products such as ceramics, metals, polymers, and cemented carbides. Modelling and simulation as…

Materials Science · Physics 2023-02-13 Min Yi , Wenxuan Wang , Ming Xue , Qihua Gong , Bai-Xiang Xu

Sintering is a widespread manufacturing process, accounting for a significant portion of global energy expenditure. However, controlling this process has been mostly a trial-and-error process, being costly in both time and money. The recent…

Materials Science · Physics 2025-10-23 Marco Seiz , Tomohiro Takaki

Phase field simulations play a key role in the understanding of microstructure evolution in additive manufacturing. However, they have been found extremely computationally expensive. One of the reasons is the small time step requirement to…

Computational Physics · Physics 2025-08-01 Chaoqian Yuan , Chinnapat Panwisawas , Ye Lu

A symmetric phase field model is used to study wavelength selection in two dimensions. We study the problem in a finite system using a two-pronged approach. First we construct an action and, minimizing this, we obtain the most probable…

Statistical Mechanics · Physics 2009-11-11 R. N. Costa Filho , J. M. Kosterlitz , Enzo Granato

We review how phase-field models contributed to the understanding of various aspects of crystal nucleation including homogeneous and heterogeneous processes, and their role in microstructure evolution. We recall results obtained both by the…

Sintering is a pivotal technology for processing ceramic and metallic powders into solid objects. A profound understanding of microstructure evolution during sintering is essential for manufacturing products with tailored properties. While…

Materials Science · Physics 2024-12-06 Qingcheng Yang , Arkadz Kirshtein

A phase-field formulation is introduced to simulate quantitatively microstructural pattern formation in alloys. The thin-interface limit of this formulation yields a much less stringent restriction on the choice of interface thickness than…

Materials Science · Physics 2016-08-31 Alain Karma

Three different topics in phase-field modelling of solidification are discussed, with particular emphasis on the limitations of the currently available modelling approaches. First, thin-interface limits of two-sided phase-field models are…

Materials Science · Physics 2015-05-18 Mathis Plapp

A numerical model able to simulate solid-state constrained sintering is presented. The model couples an existing kinetic Monte Carlo (kMC) model for free sintering with a finite element model (FEM) for calculating stresses on a…

Materials Science · Physics 2016-05-10 R. Bjørk , H. L. Frandsen , N. Pryds

Solidification is an important process in many alloy processing routes. The solidified microstructure of alloys is usually made up of dendrites, eutectics or a combination of both. The evolving morphologies are largely determined by the…

Materials Science · Physics 2024-12-17 Marco Seiz , Michael Kellner , Britta Nestler

In this research, atomistic molecular dynamics simulations are combined with mesoscopic phase-field computational methods in order to investigate phase-transformation in polycrystalline Aluminum microstructure. In fact, microstructural…

Materials Science · Physics 2019-07-03 Mehrdad Yousefi

Solid-state dewetting is the process by which thin solid films break up and retract on a substrate, forming nanostructures. While dewetting of single-crystalline films is understood as a surface-energy-driven process mediated by surface…

Materials Science · Physics 2026-02-25 Paul Hoffrogge , Nils Becker , Daniel Schneider , Britta Nestler , Axel Voigt , Marco Salvalaglio

Computational modeling of faulting processes is an essential tool for understanding earthquake mechanics but remains challenging due to the structural and material complexities of fault zones. The phase-field method has recently enabled…

Geophysics · Physics 2025-03-11 Fan Fei , Md Shumon Mia , Ahmed E. Elbanna , Jinhyun Choo

In the last two decades, many phase-field models for solid-state sintering have been published. Two groups of models have emerged, with and without the contribution of rigid body motion. This paper first describes the previously published…

Materials Science · Physics 2023-02-03 Marco Seiz

In this paper the development of a physically consistent phase-field theory of solidification shrinkage is presented. The coarse-grained hydrodynamic equations are derived directly from the N-body Hamiltonian equations in the framework of…

Materials Science · Physics 2020-02-28 Gyula I. Toth , Wenyue Ma
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