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Modeling hydrogen embrittlement (HE) is a long-standing engineering challenge, which has experienced significant developments in recent years. Yet, there is a gap in modeling the effect of the kinetics of hydrogen segregation at…

Materials Science · Physics 2026-04-08 Abdelrahman Hussein , Yann Charles , Jukka Kömi , Vahid Javaheri

We present a phase field formulation for fracture in functionally graded materials (FGMs). The model builds upon homogenization theory and accounts for the spatial variation of elastic and fracture properties. Several paradigmatic case…

Materials Science · Physics 2019-04-19 Hirshikesh , Sundararajan Natarajan , Ratna K. Annabattula , Emilio Martínez-Pañeda

Phase field fracture models have seen widespread application in the last decade. Among these applications, its use to model the evolution of fatigue cracks has attracted particular interest, as fatigue damage behaviour can be predicted for…

Computational Engineering, Finance, and Science · Computer Science 2023-04-26 P. K. Kristensen , A. Golahmar , E. Martínez-Pañeda , C. F. Niordson

The propagation of a 3D crack in an heterogeneous material is studied using a phase field model. It is shown that in the case of randomly distributed inclusions of soft material in a matrix, the nature of the distribution has little effect…

Materials Science · Physics 2025-03-11 Hervé Henry

An electro-chemo-mechanical phase-field formulation is developed to simulate pitting and stress corrosion in polycrystalline materials. The formulation incorporates dependencies of mechanical properties and corrosion potential on…

Computational Engineering, Finance, and Science · Computer Science 2024-04-01 M. Makuch , S. Kovacevic , M. R. Wenman , E. Martínez-Pañeda

Paints and coatings undergo a variety of physical and chemical changes under environmental exposures. Accurate prediction of these changes is important for the applications of coatings. This work presents a novel approach to modeling…

Soft Condensed Matter · Physics 2024-10-29 Ambesh Gupta , Soumyadipta Maiti , Parvesh Saini , Surabhi Srivastava , Shankar Kausley , Beena Rai

The problem of a crack impinging on an interface has been thoroughly investigated in the last three decades due to its important role in the mechanics and physics of solids. In this investigation, this problem is revisited in view of the…

Materials Science · Physics 2017-05-24 Marco Paggi , Jose Reinoso

We present a compelling finite element framework to model hydrogen assisted fatigue by means of a hydrogen- and cycle-dependent cohesive zone formulation. The model builds upon: (i) appropriate environmental boundary conditions, (ii) a…

Materials Science · Physics 2017-11-29 Susana del Busto , Covadonga Betegón , Emilio Martínez-Pañeda

A field theory is presented for predicting damage and fracture in quasi brittle materials incorporating effects of irreversible (plastic) deformation as well as elastic moduli that soften with damage. The new observation made here is that…

Materials Science · Physics 2026-03-17 Hayden Bromley , Robert Lipton

Hydrogen threatens the structural integrity of metals and thus predicting hydrogen-material interactions is key to unlocking the role of hydrogen in the energy transition. Quantifying the interplay between material deformation and hydrogen…

Computational Engineering, Finance, and Science · Computer Science 2025-03-04 A. Díaz , J. M. Alegre , I. I. Cuesta , E. Martínez-Pañeda

Cracking of rocks and rock-like materials exhibits a rich variety of patterns where tensile (mode I) and shear (mode II) fractures are often interwoven. These mixed-mode fractures are usually cohesive (quasi-brittle) and frictional.…

Geophysics · Physics 2021-01-12 Fan Fei , Jinhyun Choo

In the phase-field modeling of brittle fracture, anisotropic constitutive assumptions for the degradation of stored elastic energy due to fracture are crucial to preventing cracking in compression and obtaining physically sound numerical…

Numerical Analysis · Mathematics 2018-05-22 Fei Zhang , Weizhang Huang , Xianping Li , Shicheng Zhang

We investigate the role of microstructural bridging on the fracture toughness of composite materials. To achieve this, a new computational framework is presented that integrates phase field fracture and cohesive zone models to simulate…

Applied Physics · Physics 2022-01-11 W. Tan , E. Martínez-Pañeda

This study presents a novel coupled mechano-electro-chemical formulation for predicting stress corrosion cracking (SCC) phenomena in steel structures using the phase field method. SCC is a complex damage process that arises from the…

Computational Engineering, Finance, and Science · Computer Science 2025-06-09 M. Askari , P. Broumand , M. Javidi

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

Hydrogen enhanced cracking is one of the many failure mechanisms in metals depending on the corrosive environment. In the presented work, a multiscale constitutive model has been presented for hydrogen enhanced intergranular cracking in…

Materials Science · Physics 2019-10-10 M Amir Siddiq , Salah Rahimi

A model for corrosion-induced cracking of reinforced concrete subjected to non-uniform chloride-induced corrosion is presented. The gradual corrosion initiation of the steel surface is investigated by simulating chloride transport…

Computational Engineering, Finance, and Science · Computer Science 2023-12-12 E. Korec , M. Jirasek , H. S. Wong , E. Martínez-Pañeda

Brittle materials subjected to thermal shocks experience strong temperature gradients that in turn give rise to mechanical stresses that can be large enough to induce fracture. This work presents a complete model for phase-field fracture…

Computational Physics · Physics 2026-02-11 Bo Zeng , John E. Dolbow

The pattern development of multiple cracks in extremely anisotropic solids such as bilayer or multilayer two-dimensional (2D) crystals contains rich physics, which, however, remains largely unexplored. We studied crack interaction across…

Materials Science · Physics 2024-02-13 Shizhe Feng , Xiaodong Zheng , Pengjie Shi , Thuc Hue Ly , Jiong Zhao , Zhiping Xu

Modeling environmental ecosystems is essential for effective resource management, sustainable development, and understanding complex ecological processes. However, traditional data-driven methods face challenges in capturing inherently…

Machine Learning · Computer Science 2025-04-08 Runlong Yu , Shengyu Chen , Yiqun Xie , Huaxiu Yao , Jared Willard , Xiaowei Jia