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Hydrogen-induced multi-spot corrosion on the surface of polycrystalline rare metals is a complex process, which involves the interactions between phases (metal, hydride and oxide), grain orientations, grain boundaries, and corrosion spots.…

This paper proposes a phase field model (PFM) for describing hydraulic fracture propagation in transversely isotopic media. The coupling between the fluid flow and displacement fields is established according to the classical Biot…

Geophysics · Physics 2023-09-11 Shuwei Zhou , Xiaoying Zhuang

Over the past few decades, the phase-field method for fracture has seen widespread appeal due to the many benefits associated with its ability to regularize a sharp crack geometry. Along the way, several different models for including the…

Computational Engineering, Finance, and Science · Computer Science 2023-05-15 Andre Costa , Tianchen Hu , John Dolbow

In the last ten years, the phase-field method has gained much attention as a novel method to simulate fracture due to its straightforward way allowing to cover crack initiation and propagation without additional conditions. More recently,…

Materials Science · Physics 2023-05-31 Martha Kalina , Tom Schneider , Jörg Brummund , Markus Kästner

The present contribution proposes a thermodynamically consistent model for the simulation of the ductile damage. The model couples the phase field method of fracture to the Armstrong-Frederick plasticity model with kinematic hardening. The…

Materials Science · Physics 2021-06-07 Serhat Aygün , Tillmann Wiegold , Sandra Klinge

The main aim of this three-part work is to provide a unified consistent framework for the phase-field modeling of cohesive fracture. In this first paper we establish the mathematical foundation of a cohesive phase-field model by proving a…

Analysis of PDEs · Mathematics 2025-10-13 Roberto Alessi , Francesco Colasanto , Matteo Focardi

We propose a novel phase-field model to predict elastic microphase separation in polymer gels. To this end, we extend the Cahn-Hilliard free-energy functional to incorporate an elastic strain energy and a coupling term. These contributions…

Materials Science · Physics 2025-05-05 Hamza Oudich , Pietro Carrara , Laura De Lorenzis

Fracture is a ubiquitous phenomenon in most composite engineering structures, and is often the responsible mechanism for catastrophic failure. Over the past several decades, many approaches have emerged to model and predict crack failure.…

Mesoscale and Nanoscale Physics · Physics 2025-06-06 Vinamra Agrawal , Brandon Runnels

Understanding the nature of brittle failure in ferroelectric materials is essential, but difficult due to the complex interaction between mechanical and electrical concentrated fields near the crack tip. In this work, an extended…

Materials Science · Physics 2024-05-22 Chang Liu , Yu Tan , Yong Zhang , Zhaoyi Liu , Takahiro Shimada , Xiangyu Li , Jie Wang

A novel variational framework to model the fatigue behavior of brittle materials based on a phase-field approach to fracture is presented. The standard regularized free energy functional is modified introducing a fatigue degradation…

Materials Science · Physics 2020-06-04 P. Carrara , M. Ambati , R. Alessi , L. De Lorenzis

In this paper, we propose a novel, thermodynamically consistent phase field model to simulate the deformation and breakup of a ferrodroplet that is immersed in a viscous medium and subject to an applied uniform magnetic field. Instead of…

Fluid Dynamics · Physics 2017-10-31 Feng Bai , Rui Li , Xiaofeng Yang , Xiaoming He , Cheng Wang

We develop and demonstrate the first general computational tool for finite deformation static and dynamic dislocation mechanics. A finite element formulation of finite deformation (Mesoscale) Field Dislocation Mechanics theory is presented.…

Materials Science · Physics 2020-06-24 Rajat Arora , Xiaohan Zhang , Amit Acharya

The phase-field model (PFM) represents the crack geometry in a diffusive way without introducing sharp discontinuities. This feature enables PFM to effectively model crack propagation compared with numerical methods based on discrete crack…

Computational Engineering, Finance, and Science · Computer Science 2019-02-18 Shuwei Zhou , Timon Rabczuk , Xiaoying Zhuang

Hydrogen embrittlement (HE) affects all major high-strength structural materials and as such is a major impediment to lightweighting e.g. vehicles and help reduce carbon-emissions and reach net-zero. The high-strength 7xxx series aluminium…

This article presents a novel, robust and efficient framework for fatigue crack-propagation that combines the principles of Linear Elastic Fracture Mechanics (LEFM) with phase-field fracture (PFF). Contrary to cycle-by-cycle PFF approaches,…

Materials Science · Physics 2025-09-12 M. Castillón , I. Romero , J. Segurado

An adaptive phase field method is proposed for crack propagation in brittle materials under quasi-static loading. The adaptive refinement is based on the recovery type error indicator, which is combined with the quadtree decomposition. Such…

Numerical Analysis · Mathematics 2019-04-04 Hirshikesh , C Jansari , K Kannan , RK Annabattula , S Natarajan

An estimate of the effective toughness of heterogeneous materials is proposed based on the Phase Field Fracture model implemented in an FFT homogenization solver. The estimate is based on the simulation of the deformation of representative…

Materials Science · Physics 2025-08-12 Pedro Aranda , Javier Segurado

We develop and analyse the first second-order phase-field model to combine melting and dissolution in multi-component flows. This provides a simple and accurate way to simulate challenging phase-change problems in existing codes.…

Computational Physics · Physics 2020-12-09 Eric W. Hester , Louis-Alexandre Couston , Benjamin Favier , Keaton J. Burns , Geoffrey M. Vasil

The enforcement of global energy conservation in phase-field fracture simulations has been an open problem for the last 25 years. Specifically, the occurrence of unstable fracture is accompanied by a loss in total potential energy, which…

Materials Science · Physics 2026-01-01 Juan Michael Sargado , Joachim Mathiesen

Engineering alloys generally exhibit multi-phase microstructures. For simulating their microstructure evolution during solid-state phase transformation, CALPHAD-guided multi-phase-field models coupled with micro-mechanics have proven to be…

Materials Science · Physics 2023-01-05 Sourav Chatterjee , Daniel Schwen , Nele Moelans
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