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Related papers: A multiple scales approach to crack front waves

200 papers

The failure of materials and interfaces is mediated by cracks, nearly singular dissipative structures that propagate at velocities approaching the speed of sound. Crack initiation and subsequent propagation -- the dynamic process of…

Materials Science · Physics 2015-06-15 Eran Bouchbinder , Tamar Goldman , Jay Fineberg

In this paper we study dispersive wave equation using the method of multiple scales (MMS) and perform several numerical tests to investigate its accuracy. The key feature of our MMS solution is the linearity of the amplitude equation and…

Numerical Analysis · Mathematics 2021-03-29 David Juhasz , Per Kristen Jakobsen

We address the propagation into an unstable state of a localised disturbance in a forward-backward diffusion pseudo-parabolic equation. Three asymptotic regimes are distinguished as t tends to infinity, the first being a regime ahead of the…

Analysis of PDEs · Mathematics 2016-05-27 C. M. Cuesta , J. R. King

Crack front waves are localized waves that propagate along the leading edge of a crack. They are generated by the interaction of a crack with a localized material inhomogeneity. We show that front waves are nonlinear entities that transport…

Materials Science · Physics 2009-11-07 E. Sharon , G. Cohen , J. Fineberg

Predicting crack trajectories in brittle solids remains an open challenge in fracture mechanics due to the non-local nature of crack propagation and the way cracks modify their surrounding medium. Here, we develop a framework for…

Soft Condensed Matter · Physics 2025-02-25 Oran Szachter , Emmanuel Siefert , Mokhtar Adda-Bedia , Eran Sharon , Michael Moshe

For scattering problems of time-harmonic waves, the boundary integral equation (BIE) methods are highly competitive, since they are formulated on lower-dimension boundaries or interfaces, and can automatically satisfy outgoing radiation…

Numerical Analysis · Mathematics 2018-04-24 Wangtao Lu , Ya Yan Lu , Jianliang Qian

In the context of elastic wave propagation in damaged solids, an analytical approach for scattering of antiplane waves by two-dimensional periodic arrays of cracks is developed. Before considering the study of arrays of cracks, the…

Materials Science · Physics 2013-02-07 Mihai Caleap

Reaction-diffusion equations (RDEs) are often derived as continuum limits of lattice-based discrete models. Recently, a discrete model which allows the rates of movement, proliferation and death to depend upon whether the agents are…

Dynamical Systems · Mathematics 2021-05-19 Yifei Li , Peter van Heijster , Matthew J. Simpson , Martin Wechselberger

We show that for the simulation of crack propagation in quasi-brittle, two-dimensional solids, very good results can be obtained with an embedded strong discontinuity quadrilateral finite element that has incompatible modes. Even more…

Numerical Analysis · Mathematics 2021-09-08 A. Stanic , B. Brank , A. Ibrahimbegovic , H. G. Matthies

We present a variational reduced-order model for three-dimensional coplanar propagation of sharp cracks in heterogeneous perfectly brittle solids under mixed-mode I+II+III loading. The approach connects the variational fracture formulation…

Materials Science · Physics 2026-05-14 Serafim Egorov , Antoine Sanner , Jean Sulem , Lars Pastewka , Mathias Lebihain

Crack propagation is studied numerically using a continuum phase-field approach to mode III brittle fracture. The results shed light on the physics that controls the speed of accelerating cracks and the characteristic branching instability…

Materials Science · Physics 2009-11-10 Alain Karma , Alexander E. Lobkovsky

The analogy between frictional cracks, propagating along interfaces in frictional contact, and ordinary cracks in bulk materials is important in various fields. We consider a stress-controlled frictional crack propagating at a velocity…

Materials Science · Physics 2025-04-08 Efim A. Brener , Eran Bouchbinder

Extremely asymmetrical scattering (EAS) is a new type of Bragg scattering in thick, slanted, periodic gratings. It is realised when the scattered wave propagates parallel to the front boundary of the grating. Its most important feature is…

Optics · Physics 2007-05-23 T. A. Nieminen , D. K. Gramotnev

The paper presents a model of a dynamic crack with a wavy surface. So far, theoretical analysis of crack front waves has been performed only for in-plane perturbations of the crack front. In the present paper, generalisation is given to a…

Analysis of PDEs · Mathematics 2012-06-06 J. R. Willis , N. V. Movchan , A. B. Movchan

The dynamics of planar crack fronts in hetergeneous media near the critical load for onset of crack motion are investigated both analytically and by numerical simulations. Elasticity of the solid leads to long range stress transfer along…

Disordered Systems and Neural Networks · Physics 2009-10-30 Sharad Ramanathan , Daniel S. Fisher

We present here a semi-analytical solution of the problem of particle acceleration at non-linear shock waves with a free escape boundary at some location upstream. This solution, besides allowing us to determine the spectrum of particles…

High Energy Astrophysical Phenomena · Physics 2014-11-20 D. Caprioli , E. Amato , P. Blasi

Crack front waves (FWs) are dynamic objects that propagate along moving crack fronts in 3D materials. We study FW dynamics in the framework of a 3D phase-field framework that features a rate-dependent fracture energy $\Gamma(v)$ ($v$ is the…

Materials Science · Physics 2023-10-05 Sanhita Das , Yuri Lubomirsky , Eran Bouchbinder

We employ a recently developed model that allows the study of two-dimensional brittle crack propagation under fixed grip boundary conditions. The crack development highlights the importance of voids which appear ahead of the crack as…

Disordered Systems and Neural Networks · Physics 2015-06-12 Itamar Procaccia , Jacques Zylberg

We analyze a piece-wise linear elastic model for the propagation of a crack in a stripe geometry under mode III conditions, in the absence of dissipation. The model is continuous in the propagation direction and discrete in the…

Materials Science · Physics 2009-11-11 T. M. Guozden , E. A. Jagla

We model the diffusive shock acceleration of particles in a system of two colliding shock waves and present a method to solve the time-dependent problem analytically in the test-particle approximation and high energy limit. In particular,…

High Energy Astrophysical Phenomena · Physics 2020-05-06 Thibault Vieu , Stefano Gabici , Vincent Tatischeff