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The difficulties in dealing with discontinuities related to a sharp crack are overcome in the phase-field approach for fracture by modeling the crack as a diffusive object being described by a continuous field having high gradients. The…

Computational Engineering, Finance, and Science · Computer Science 2023-12-05 Sindhu Nagaraja , Mohamed Elhaddad , Marreddy Ambati , Stefan Kollmannsberger , Laura De Lorenzis , Ernst Rank

We present a continuum theory to describe elastically induced phase transitions between coherent solid phases. In the limit of vanishing elastic constants in one of the phases, the model can be used to describe fracture on the basis of the…

Materials Science · Physics 2009-11-13 R. Spatschek , C. Mueller-Gugenberger , E. Brener , B. Nestler

Phase-field modeling -- a continuous approach to discontinuities -- is gaining popularity for simulating rock fractures due to its ability to handle complex, discontinuous geometry without an explicit surface tracking algorithm. None of the…

Geophysics · Physics 2022-11-24 Fan Fei , Jinhyun Choo , Chong Liu , Joshua A. White

Event skeleton generation, aiming to induce an event schema skeleton graph with abstracted event nodes and their temporal relations from a set of event instance graphs, is a critical step in the temporal complex event schema induction task.…

Computation and Language · Computer Science 2023-05-30 Fangqi Zhu , Lin Zhang , Jun Gao , Bing Qin , Ruifeng Xu , Haiqin Yang

This article proposes an open-source implementation of a phase-field model for brittle fracture using a recently developed finite element toolbox, Gridap in Julia. The present work exploits the advantages of both the phase-field model and…

Computational Engineering, Finance, and Science · Computer Science 2021-09-14 Mohammad Masiur Rahaman

We propose a full 3D benchmark problem for brittle fracture based on experiments as well as a validation in the context of phase-field models. The example consists of a series of four-point bending tests on graphite specimens with sharp…

Computational Engineering, Finance, and Science · Computer Science 2020-04-22 Lisa Hug , Stefan Kollmannsberger , Zohar Yosibash , Ernst Rank

Soft polymers are ubiquitous materials in nature and as engineering materials with properties varying from rate-independent to rate-dependent. Current fracture toughness measures are non-unique for rate-dependent soft materials for varying…

Soft Condensed Matter · Physics 2026-03-17 Aditya Konale , Vikas Srivastava

Following the so-called Cracking Elements Method (CEM), recently presented in \cite{Yiming:14,Yiming:16}, we propose a novel Galerkin-based numerical approach for simulating quasi-brittle fracture, named Global Cracking Elements Method…

Computational Engineering, Finance, and Science · Computer Science 2019-08-20 Yiming Zhang , Herbert A. Mang

The phase-field method has become popular for the numerical modeling of fluid-filled fractures, thanks to its ability to represent complex fracture geometry without algorithms. However, the algorithm-free representation of fracture geometry…

Geophysics · Physics 2024-11-19 Fan Fei , Jinhyun Choo

A novel phase-field for ductile fracture model is presented. The model is developed within a consistent variational framework in the context of finite-deformation kinematics. A novel coalescence dissipation introduces a new coupling…

Materials Science · Physics 2021-03-24 Tianchen Hu , Brandon Talamini , Andrew J. Stershic , Michael R. Tupek , John E. Dolbow

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

A moving mesh finite element method is studied for the numerical solution of a phase-field model for brittle fracture. The moving mesh partial differential equation approach is employed to dynamically track crack propagation. Meanwhile, the…

Numerical Analysis · Mathematics 2018-01-17 Fei Zhang , Weizhang Huang , Xianping Li , Shicheng Zhang

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

Variational phase field fracture models are now widely used to simulate crack propagation in structures. A critical aspect of these simulations is the correct determination of the propagation threshold of pre-existing cracks, as it highly…

Computational Engineering, Finance, and Science · Computer Science 2025-02-07 Flavien Loiseau , Veronique Lazarus

In this paper a composite model for earthquake rupture initiation and propagation is proposed. The model includes aspects of damage mechanics, fiber-bundle models, and slider-block models. An array of elements is introduced in analogy to…

Geophysics · Physics 2010-07-14 G. Yakovlev , J. D. Gran , D. L. Turcotte , J. B. Rundle , W. Klein

We develop a novel constitutive modeling approach for the analysis of fracture propagation in quasi-brittle materials using the Material Point Method. The kinematics of constitutive models is enriched with an additional mode of localized…

Computational Physics · Physics 2014-06-06 Giang Dinh Nguyen

The goal of the current work is to explore direction-dependent damage initiation and propagation within an arbitrary anisotropic solid. In particular, we aim at developing anisotropic cohesive phase-field (PF) damage models by extending the…

Computational Engineering, Finance, and Science · Computer Science 2022-05-23 Shahed Rezaei , Ali Harandi , Tim Brepols , Stefanie Reese

A new model is presented to predict hydrogen-assisted fatigue. The model combines a phase field description of fracture and fatigue, stress-assisted hydrogen diffusion, and a toughness degradation formulation with cyclic and hydrogen…

Computational Engineering, Finance, and Science · Computer Science 2024-05-21 C. Cui , P. Bortot , M. Ortolani , E. Martínez-Pañeda

We investigate the potential of quasi-Newton methods in facilitating convergence of monolithic solution schemes for phase field fracture modelling. Several paradigmatic boundary value problems are addressed, spanning the fields of…

Numerical Analysis · Mathematics 2019-12-19 Philip K. Kristensen , Emilio Martínez-Pañeda

Understanding and controlling fracture propagation is one of the most challenging engineering problems, especially in the oil and gas sector, groundwater hydrology and geothermal energy applications. Predicting the fracture orientation…

Materials Science · Physics 2023-04-04 Ramesh Kannan Kandasami , Charalampos Konstantinou , Giovanna Biscontin