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We present a generalised phase field-based formulation for predicting fatigue crack growth in metals. The theoretical framework aims at covering a wide range of material behaviour. Different fatigue degradation functions are considered and…

Computational Engineering, Finance, and Science · Computer Science 2021-11-24 Z. Khalil , A. Y. Elghazouli , 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

For the fatigue life of thin-walled components, not only fatigue crack initiation, but also crack growth is decisive. The phase-field method for fracture is a powerful tool to simulate arbitrary crack phenomena. Recently, it has been…

Materials Science · Physics 2021-04-07 Martha Seiler , Sören Keller , Nikolai Kashaev , Benjamin Klusemann , Markus Kästner

As a model of composite material, the fiber bundle model has been chosen -where a bundle of fibers is subjected to external load and fibers have distributed thresholds. For different loading conditions, such a system shows few precursors…

Materials Science · Physics 2015-05-19 Srutarshi Pradhan

Compressive-shear fracture is commonly observed in rock-like materials. However, this fracture type cannot be captured by current phase field models (PFMs), which have been proven an effective tool for modeling fracture initiation,…

Computational Engineering, Finance, and Science · Computer Science 2023-08-14 Shuwei Zhou , Xiaoying Zhuang , Timon Rabczuk

In this contribution, a novel framework for simulating mixed-mode failure in rock is presented. Based on a hybrid phase-field model for mixed-mode fracture, separate phase-field variables are introduced for tensile (mode I) and shear (mode…

Computational Engineering, Finance, and Science · Computer Science 2023-12-05 Lisa Hug , Martin Potten , Georg Stockinger , Kurosch Thuro , Stefan Kollmannsberger

This work presents a comprehensive phase-field framework for modeling anisotropic viscoelastic-viscoplastic fracture in short fiber-reinforced polymer (SFRP) composites under hygrothermal environments at finite deformation. The constitutive…

Computational Engineering, Finance, and Science · Computer Science 2026-03-04 Behrouz Arash , Shadab Zakavati , Timon Rabczuk

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

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

This paper investigates the effects of plasticity on the effective fracture toughness. A layered material is considered as a modelling system. An elastic-plastic phase-field model and a surfing boundary condition are used to study how the…

Computational Engineering, Finance, and Science · Computer Science 2020-10-15 Stella Brach

The phase field approach to modeling fracture uses a diffuse damage field to represent a crack. This addresses the singularities that arise at the crack tip in computations with sharp interface models, mollifying some of the difficulties…

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

In this paper, we extend a micromechanics-based phase-field framework for fatigue fracture to incorporate cyclic plasticity with ratcheting. This mechanism is particularly relevant for low-cycle fatigue, where the accumulation of inelastic…

Applied Physics · Physics 2026-02-05 Mina Sarem , Nuhamin Eshetu Deresse , Els Verstrynge , Stijn François

Understanding the role played by the microstructure of materials on their macroscopic failure properties is an important challenge in solid mechanics. Indeed, when a crack propagates at a heterogeneous brittle interface, the front is…

Materials Science · Physics 2015-11-09 Sylvain Patinet , L Alzate , E Barthel , D Dalmas , D Vandembroucq , V Lazarus

We propose a variational phase-field model of fracture capable of accounting for arbitrary closed convex strength domains. Unlike traditional models based on Ambrosio and Tortorelli regularization, the phase-field variable does not affect…

Applied Physics · Physics 2025-07-01 Blaise Bourdin , Jean-Jacques Marigo , Corrado Maurini , Camilla Zolesi

This study evaluates four widely used fracture simulation methods, comparing their computational expenses and implementation complexities within the Finite Element (FE) framework when employed on heterogeneous solids. Fracture methods…

Computational Engineering, Finance, and Science · Computer Science 2024-11-19 Rasoul Najafi Koopas , Shahed Rezaei , Natalie Rauter , Richard Ostwald , Rolf Lammering

Brittle materials fail catastrophically. In consequence of their limited flaw-tolerance, failure occurs by localized fracture and is typically a dynamic process. Recently, experiments on epithelial cell monolayers have revealed that this…

Soft Condensed Matter · Physics 2017-02-07 Alessandro Lucantonio , Giovanni Noselli

Dense ceramics are irreplaceable in applications requiring high mechanical stiffness, chemical and temperature resistance and low weight. To improve their toughness, ceramics can be reinforced with elongated inclusions. Recent manufacturing…

Applied Physics · Physics 2019-06-07 Hortense Le Ferrand

Composites with high strength and high fracture resistance are desirable for structural and protective applications. Most composites, however, suffer from poor damage tolerance and are prone to unpredictable fractures. Understanding the…

Materials Science · Physics 2024-04-23 Tommaso Magrini , Chelsea Fox , Adeline Wihardja , Athena Kolli , Chiara Daraio

The mechanical behavior of composite materials is significantly influenced by their structure and constituent materials. One emerging class of composite materials is irregular network reinforced composites (NRC's), whose reinforcing phase…

Soft Condensed Matter · Physics 2025-10-14 Chelsea Fox , Tommaso Magrini , Chiara Daraio
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