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Related papers: Crack propagation as a free boundary problem

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We examine the fracture mechanics of tearing graphene. We present a molecular dynamics simulation of the propagation of cracks in clamped, free-standing graphene as a function of the out-of-plane force. The geometry is motivated by…

Mesoscale and Nanoscale Physics · Physics 2015-06-16 Maria J. B. Moura , Michael Marder

A continuum model of fracture that describes, in principle, the propagation and interaction of arbitrary distributions of cracks and voids with evolving topology without a fracture criterion is developed. It involves a 'law of motion' for…

Materials Science · Physics 2020-04-22 Amit Acharya

Ever since the very first human-made knapped tools, the control of fracture propagation in brittle materials has been a vector of technological development. Nowadays, a broad range of applications relies on crack propagation control, from…

The problem of partially hinged and partially free rectangular plate that aims to represent a suspension bridge subject to some external forces (for example the wind) is considered in order to model and simulate the unstable end behavior.…

Numerical Analysis · Mathematics 2024-04-17 Raj Narayan Dhara , Krzysztof E. Rutkowski , Katarzyna Szulc

We consider a discretized version of the quenched Edwards-Wilkinson model for the propagation of a driven interface through a random field of obstacles. Our model consists of a system of ordinary differential equations on a $d$-dimensional…

Probability · Mathematics 2016-08-02 Patrick W. Dondl , Michael Scheutzow

We present a systematic study of the effect of crack blunting on subsequent crack propagation and dislocation emission. We show that the stress intensity factor required to propagate the crack is increased as the crack is blunted by up to…

mtrl-th · Physics 2009-10-30 J. Schiøtz , L. M. Canel , A. E. Carlsson

A number of simplified dynamical problems is studied in an attempt to clarify some of the mechanisms leading to turbulence and the existing proposals to control this transition. A simplified set of boundary layer equations displays a…

Fluid Dynamics · Physics 2007-05-23 R. Vilela Mendes

We consider the motion of planar phase-transition fronts in first-order phase transitions of the Universe. We find the steady state wall velocity as a function of a friction coefficient and thermodynamical parameters, taking into account…

Cosmology and Nongalactic Astrophysics · Physics 2012-08-17 Ariel Megevand , Alejandro D. Sanchez

We consider atomistic systems consisting of interacting particles arranged in atomic lattices whose quasi-static evolution is driven by time-dependent boundary conditions. The interaction of the particles is modeled by classical interaction…

Analysis of PDEs · Mathematics 2022-11-01 Rufat Badal , Manuel Friedrich , Joscha Seutter

We discuss a numerical method for convection-diffusion-reaction problems with a free boundary in 1D. The method is based on the numerical modelling of the interface evolution, the transformation to a fixed domain problem and the…

Numerical Analysis · Mathematics 2009-09-03 Gabriela Kacurova

This paper presents an algorithm for the efficient simulation of ductile crack propagation through heterogeneous structures, as e.g. metallic microstructures, which are given as voxel data. These kinds of simulations are required for e.g.,…

Numerical Analysis · Mathematics 2022-02-23 Dennis Wingender , Daniel Balzani

We study transmission problems with free interfaces from one random medium to another. Solutions are required to solve distinct partial differential equations, $\mbox{L}_{+}$ and $\mbox{L}_{-}$, within their positive and negative sets…

Analysis of PDEs · Mathematics 2015-10-14 Marcelo Amaral , Eduardo V. Teixeira

We describe the resulting spatiotemporal dynamics when a homogeneous equilibrium loses stability in a spatially extended system. More precisely, we consider reaction-diffusion systems, assuming only that the reaction kinetics undergo a…

Analysis of PDEs · Mathematics 2023-10-23 Montie Avery

When a crack interacts with material heterogeneities, its front distorts and adopts complex tortuous configurations that are reminiscent of the energy barriers encountered during crack propagation. As such, the study of crack front…

Materials Science · Physics 2023-01-03 Mathias Lebihain , Thibault Roch , Jean-François Molinari

The crack phase field model has been well established and validated for a variety of complex crack propagation patterns within a homogeneous medium under either tensile or shear loading. However, relatively less attention has been paid to…

Materials Science · Physics 2018-09-14 Heeyeong Jeong , Stefano Signetti , Tong-Seok Han , Seunghwa Ryu

We study Mode I crack propagation in amorphous material via a molecular dynamics simulation of a binary alloy with pairwise central-force interactions. We find that when the system is subjected to constant displacement after introduction of…

Materials Science · Physics 2007-05-23 Tsviki Y. Hirsh , David A. Kessler

This paper deals with the evolution equation of a curve obtained as the sharp interface limit of a non-linear system of two reaction-diffusion PDEs. This system was introduced as a phase-field model of (crawling) motion of eukaryotic cells…

Analysis of PDEs · Mathematics 2016-03-23 Matthew S. Mizuhara , Leonid Berlyand , Volodymyr Rybalko , Lei Zhang

This paper is concerned with the problem of a semi-infinite crack steadily propagating in an elastic solid with microstructures subject to antiplane loading applied on the crack surfaces. The loading is moving with the same constant…

Mathematical Physics · Physics 2012-07-17 G. Mishuris , A. Piccolroaz , E. Radi

We complete the description, initiated in [6], of a free boundary travelling at constant speed in a half plane, where the propagation is controlled by a line having a large diffusion on its own. The main result of this work is that the free…

Analysis of PDEs · Mathematics 2020-04-01 Luis Caffarelli , Jean-Michel Roquejoffre

We study the Stokes problem in a bounded planar domain $\Omega$ with a friction type boundary condition that switches between a slip and no-slip stage. Unlike our previous work [6], in the present paper the threshold value may depend on the…

Analysis of PDEs · Mathematics 2016-01-22 Jaroslav Haslinger , Jan Stebel