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Vertex and front-tracking methods for the modeling of microstructure evolution at the solid state: a brief review

Marc Bernacki

TL;DR

The paper surveys front-tracking strategies for mesoscopic microstructure evolution, contrasting Vertex frameworks with broader front-tracking approaches to reveal how explicit grain-boundary discretization enhances spatial resolution and physical fidelity. It traces the evolution from early 2D vertex models that ignore curvature toward curvature-driven and 3D-enriched formulations, including real and virtual vertices, micro-stepping, and pinning phenomena such as Smith–Zener effects. It also maps enrichment avenues—anisotropic mobility, torque terms, and crystal-plasticity coupling—and compares Vertex-centric methods with alternative FT frameworks and topology-preserving remeshing techniques. The discussion highlights both the computational efficiency and the challenges in handling complex topologies and intragranular phenomena, pointing to TRM and related 3D FE-based front-tracking as promising directions for scalable, physically faithful microstructure simulations.

Abstract

In mesoscopic scale microstructure evolution modeling, two primary numerical frameworks are used: Front-Capturing (FC) and Front-Tracking (FT) ones. FC models, like phase-field or level-set methods, indirectly define interfaces by tracking field variable changes. On the contrary, FT models explicitly define interfaces using interconnected segments or surfaces. In historical FT methodologies, Vertex models were first developed and consider the description of the evolution of polygonal structures in terms of the motion of points where multiple boundaries meet. Globally, FT-type approaches, often associated with Lagrangian movement, enhance spatial resolution in 3D surfacic and 2D lineic problems using techniques derived from finite element meshing and remeshing algorithms. These efficient approaches, by nature, are well adapted to physical mechanisms correlated to interface properties and geometries. They also face challenges in managing complex topological events, especially in 3D. However, recent advances highlight their potential in computational efficiency and analysis of mobility and energy properties, with possible applications in intragranular phenomena.

Vertex and front-tracking methods for the modeling of microstructure evolution at the solid state: a brief review

TL;DR

The paper surveys front-tracking strategies for mesoscopic microstructure evolution, contrasting Vertex frameworks with broader front-tracking approaches to reveal how explicit grain-boundary discretization enhances spatial resolution and physical fidelity. It traces the evolution from early 2D vertex models that ignore curvature toward curvature-driven and 3D-enriched formulations, including real and virtual vertices, micro-stepping, and pinning phenomena such as Smith–Zener effects. It also maps enrichment avenues—anisotropic mobility, torque terms, and crystal-plasticity coupling—and compares Vertex-centric methods with alternative FT frameworks and topology-preserving remeshing techniques. The discussion highlights both the computational efficiency and the challenges in handling complex topologies and intragranular phenomena, pointing to TRM and related 3D FE-based front-tracking as promising directions for scalable, physically faithful microstructure simulations.

Abstract

In mesoscopic scale microstructure evolution modeling, two primary numerical frameworks are used: Front-Capturing (FC) and Front-Tracking (FT) ones. FC models, like phase-field or level-set methods, indirectly define interfaces by tracking field variable changes. On the contrary, FT models explicitly define interfaces using interconnected segments or surfaces. In historical FT methodologies, Vertex models were first developed and consider the description of the evolution of polygonal structures in terms of the motion of points where multiple boundaries meet. Globally, FT-type approaches, often associated with Lagrangian movement, enhance spatial resolution in 3D surfacic and 2D lineic problems using techniques derived from finite element meshing and remeshing algorithms. These efficient approaches, by nature, are well adapted to physical mechanisms correlated to interface properties and geometries. They also face challenges in managing complex topological events, especially in 3D. However, recent advances highlight their potential in computational efficiency and analysis of mobility and energy properties, with possible applications in intragranular phenomena.
Paper Structure (6 sections, 15 equations, 12 figures)

This paper contains 6 sections, 15 equations, 12 figures.

Table of Contents

  1. Introduction
  2. Vertex frameworks
  3. From Vertex to front-tracking then to enriched Vertex frameworks
  4. Enrichment of the Vertex approach
  5. Other front-tracking frameworks for the modeling of microstructure evolution
  6. Conclusion

Figures (12)

  • Figure 1: Successive stages in the growth of a 2D grain structure with the number of steps (proportional to the physical time). Simulation from Soares1985.
  • Figure 2: 2D Topological transformations: a) recombination (T1), b) annihilation of small three-sided grain (T2), c) elimination of a grain with two triple points (T3), d) an example of the occurrence of a T3 transformation and e) T2 transformation shown as equivalent to a sequence of T1 and T3 transformations. Source: From FlorezPhD2020 as inspired from Weygand1998First.
  • Figure 3: Schematic illustration of simulation techniques for modeling boundary migration and triple point motion. Source: Frost1988
  • Figure 4: Grain structure obtained by Weygand et al. by considering virtual vertices alongs GBs (a) and without virtual vertices (b). Source: Weygand1998First
  • Figure 5: (left side) Three-dimensional elementary processes:(a) Recombination process, (b) Tetrahedron annihilation. (right side) first 3D vertex simulations. Source: Nagai1990
  • ...and 7 more figures