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Related papers: Cohesive fracture in 1D: quasi-static evolution an…

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We address a three-dimensional model capable of describing coupled damage and plastic effects in solids at finite strains. Formulated within the variational setting of {\it generalized standard materials}, the constitutive model results…

Analysis of PDEs · Mathematics 2020-12-30 David Melching , Michael Neunteufel , Joachim Schöberl , Ulisse Stefanelli

Motivated by models of fracture mechanics, this paper is devoted to the analysis of unilateral gradient flows of the Ambrosio-Tortorelli functional, where unilaterality comes from an irreversibility constraint on the fracture density. In…

Analysis of PDEs · Mathematics 2013-10-28 Jean-Francois Babadjian , Vincent Millot

This work overviews a new, recent success of phase-field modelling: its application to predicting the evolution of the corrosion front and the associated structural integrity challenges. Despite its important implications for society,…

Chemical Physics · Physics 2024-06-24 E. Martínez-Pañeda

We propose a geometrically motivated mathematical model which reveals the key features of coastal and fluvial fragment shape evolution from the earliest stages of the abrasion. Our \textit{collisional polygon model} governs the evolution…

Mathematical Physics · Physics 2023-10-12 Balázs Havasi-Tóth , Eszter Fehér

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

We study a variational model for the quasistatic growth of cracks with fractional di- mension in brittle materials. We give a minimal set of properties of the collection of admissible cracks which ensure the existence of a quasistatic…

Optimization and Control · Mathematics 2016-02-29 Gianni Dal Maso , Marco Morandotti

Phase-field fracture models are known to overestimate the crack area, a discrepancy that compromises the accuracy of fracture predictions. This issue stems from the diffuse crack representation and numerical artifacts, such as strain…

Materials Science · Physics 2026-05-06 M. Castillón , J. Segurado , I. Romero

The modeling of cracks has been an intensely researched topic for decades - both from the mechanical as well as from the mathematics point of view. As far as the modeling of sharp cracks/interfaces is concerned, the resulting free boundary…

Analysis of PDEs · Mathematics 2022-11-24 Samira Boddin , Felix Rörentrop , Dorothee Knees , Jörn Mosler

The quasi-brittle nature of rocks challenges the basic assumptions of linear hydraulic fracture mechanics (LHFM): linear elastic fracture mechanics and smooth parallel plates lubrication fluid flow. We relax these hypotheses and investigate…

Fluid Dynamics · Physics 2021-01-28 Dong Liu , Brice Lecampion

We introduce a class of models based on near crack tip degradation of materials that can account for fracture growth under cyclic loads below the Griffith threshold. We incorporate the gradual degradation due to a cyclic load through a flow…

Materials Science · Physics 2019-06-26 Ataollah Mesgarnejad , Anahita Imanian , Alain Karma

A simple nonlocal field theory of peridynamic type is applied to model brittle fracture. The fracture evolution is shown to converge in the limit of vanishing nonlocality to classic plane elastodynamics with a running crack. The kinetic…

Analysis of PDEs · Mathematics 2020-07-30 Robert Lipton , Prashant K. Jha

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

The failure of 2D numerical cohesive granular steps collapsing under gravity are simulated for a large range of cohesion. Focussing on the cumulative displacement of the grains, and defining a displacement threshold, we establish a sensible…

Soft Condensed Matter · Physics 2022-04-01 Lydie Staron , Laurent Duchemin , Anais Abramian , Pierre-Yves Lagrée

We present an energy-preserving mechanic formulation for dynamic quasi-brittle fracture in an Eulerian-Lagrangian formulation, where a second-order phase-field equation controls the damage evolution. The numerical formulation adapts in…

Mathematical Physics · Physics 2022-02-23 Nicolas A. Labanda , Luis Espath , Victor Manuel Calo

We propose a time-space discretization of a general notion of quasistatic growth of brittle fractures in elastic bodies proposed in [13] by G. Dal Maso, G.A. Francfort, and R. Toader, which takes into account body forces and surface loads.…

Analysis of PDEs · Mathematics 2025-10-20 Alessandro Giacomini , Marcello Ponsiglione

We study three quasicontinuum approximations of a lattice model for crack propagation. The influence of the approximation on the bifurcation patterns is investigated. The estimate of the modeling error is applicable to near and beyond…

Numerical Analysis · Mathematics 2013-10-03 Xiantao Li , Pingbing Ming

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

A directed avalanche model with a control parameter is introduced to describe the transition between cohesive and noncohesive granular material. The underlying dynamics of the process can be mapped to interface growth model. In that…

Statistical Mechanics · Physics 2009-11-07 Chun-Chung Chen

We present a scalable, parallel implementation of a solver for the solution of a phase-field model for quasi-static brittle fracture. The code is available as open source. Numerical solutions in 2d and 3d with adaptive mesh refinement show…

Numerical Analysis · Mathematics 2018-06-27 Timo Heister , Thomas Wick

We derive the variational formulation of a gradient damage model by applying the energetic formulation of rate-independent processes and obtain a regularized formulation of fracture. The model exhibits different behavior at traction and…

Numerical Analysis · Mathematics 2020-12-15 Mariela Luege , Antonio Orlando