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This paper presents a computational framework for quasi-static brittle fracture in three dimensional solids. The paper set outs the theoretical basis for determining the initiation and direction of propagating cracks based on the concept of…

Computational Physics · Physics 2013-12-02 Lukasz Kaczmarczyk , Mohaddeseh Mousavi Nezhad , Chris Pearce

A model which accounts for cracking avalanches in piles of grains subject to external load is introduced and numerically simulated. The stress is stochastically transferred from higher layers to lower ones. Cracked areas exhibit various…

Disordered Systems and Neural Networks · Physics 2009-10-31 Frantisek Slanina

A mathematical continuum limit of the interaction energy of a random particle chain is shown to yield new insight into the effect of microscopic heterogeneities on macroscopic fracture laws in brittle materials. We derive a formula which…

Analysis of PDEs · Mathematics 2021-04-20 Laura Lauerbach , Anja Schlömerkemper

The earthquake-like model with a continuous distribution of static thresholds is used to describe the properties of solid friction. The evolution of the model is reduced to a master equation which can be solved analytically. This approach…

Statistical Mechanics · Physics 2008-08-06 Oleg Braun , Michel Peyrard

The analysis of standardized low cycle fatigue (LCF) experiments shows that the failure times widely scatter. Furthermore, mechanical components often fail before the deterministic failure time is reached. A possibility to overcome these…

Materials Science · Physics 2022-07-07 M. Harder , P. Lion , L. Mäde , T. Beck , H. Gottschalk

We discuss crack propagation along the interface between two dissimilar materials. The crack edge separates two states of the interface, ``stick'' and ``slip''. In the slip region we assume that the shear stress is proportional to the…

Materials Science · Physics 2016-08-31 Efim A. Brener , V. I. Marchenko

We consider a model of fragmentation of sheet by cracks that move with a velocity in preferred direction, but undergo random transverse displacements as they move. There is a non-zero probability of crack-splitting, and the split cracks…

Statistical Mechanics · Physics 2015-06-23 Deepak Dhar

We present regularity results for the crack set of a minimizer for the Griffith fracture energy, arising in the variational modeling of brittle materials. In the planar setting, we prove an epsilon-regularity theorem showing that the crack…

Analysis of PDEs · Mathematics 2025-09-16 Manuel Friedrich , Camille Labourie , Kerrek Stinson

We present a continuum phase-field model of crack propagation. It includes a phase-field that is proportional to the mass density and a displacement field that is governed by linear elastic theory. Generic macroscopic crack growth laws…

Materials Science · Physics 2009-11-07 L. O. Eastgate , J. P. Sethna , M. Rauscher , T. Cretegny , C. -S. Chen , C. R. Myers

We derive a general crack propagation law for slow brittle cracking, in two and three dimensions, using symmetry, gauge invariance, and gradient expansions. Our derivation provides explicit justification for the ``principle of local…

Condensed Matter · Physics 2009-10-22 Jennifer Hodgdon , James P. Sethna

We give a precise mathematical formulation of a variational model for the irreversible quasi-static evolution of brittle fractures proposed by G.A. Francfort and J.-J. Marigo, and based on Griffith's theory of crack growth. In the…

Analysis of PDEs · Mathematics 2009-11-07 Gianni Dal Maso , Rodica Toader

Spontaneous brittle fracture is studied based on the recently introduced model (Mishuris and Slepyan, Brittle fracture in a periodic structure with internal potential energy. Proc. Roy. Soc. A, in press). A periodic structure is considered,…

Soft Condensed Matter · Physics 2015-06-18 Mark Ayzenberg-Stepanenko , Gennady Mishuris , Leonid Slepyan

Two novel single-period cracks were observed in experiments of cutting a folded sheet with a blunt object and tearing a thin brittle sheet under the guidance of a meterstick. Additionally, we observed a period-doubling crack in the tearing…

Soft Condensed Matter · Physics 2020-12-11 Chuang-Shi Shen , Chun-Lin Du , Huan-Fang Wang , Chao Zhang

The growth of cracks combines materials science, fracture mechanics, and statistical physics. The importance of fluctuations in the crack velocity is fundamental since it signals that the crack overcomes local barriers such as tough spots…

Statistical Mechanics · Physics 2025-03-11 Tero Mäkinen , Lumi Tuokkola , Joonas Lahikainen , Ivan V. Lomakin , Juha Koivisto , Mikko J. Alava

The lifetime of most metals is limited by cyclic loads, ending in fatigue failure. The progressive growth of cracks ends up in catastrophic failure. An advanced method is presented for the determination of cyclic crack growth on the…

Materials Science · Physics 2022-08-03 S. Gabel , B. Merle , E. Bitzek , M. Göken

The phase-field method is based on the energy minimization principle which is a geometric method for modeling diffusive cracks that are popularly implemented with irreversibility based on Griffith's criterion. This method requires a…

Optimization and Control · Mathematics 2025-04-01 Tim Suchan , Chaitanya Kandekar , Wolfgang E. Weber , Kathrin Welker

A force balance condition to predict quasistatic crack paths in anisotropic brittle materials is derived from an analysis of diffuse interface continuum models that describe both short-scale failure inside a microscopic process zone and…

Materials Science · Physics 2009-11-10 Vincent Hakim , Alain Karma

At the mesoscale friction occurs through the breaking and formation of local contacts. This is often described by the earthquake-like model which requires numerical studies. We show that this phenomenon can also be described by a master…

Statistical Mechanics · Physics 2010-09-30 Oleg Braun , Michel Peyrard

When fast cracks become unstable to microscopic branching (micro-branching), fracture no longer occurs in an effective 2D medium. We follow in-plane crack front dynamics via real-time measurements in brittle gels as micro-branching unfolds…

Materials Science · Physics 2015-05-19 Itamar Kolvin , Gil Cohen , Jay Fineberg

The invasion of air into porous systems in drying processes is often localized in soft materials, such as colloidal suspensions and granular pastes, and it typically develops in the form of cracks before ordinary drying begins. To…

Soft Condensed Matter · Physics 2013-05-21 So Kitsunezaki