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Related papers: Quasi-static evolution in brittle fracture: the ca…

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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

A space-discretization for the elastic flow of inextensible curves is devised and quasi-optimal convergence of the corresponding semi-discrete problem is proved for a suitable discretization of the nonlinear inextensibility constraint.…

Numerical Analysis · Mathematics 2025-04-07 Sören Bartels , Klaus Deckelnick , Dominik Schneider

The goal of this work is to analyze a model for the rate-independent evolution of sets with finite perimeter. The evolution of the admissible sets is driven by that of a given time-dependent set, which has to include the admissible sets and…

Analysis of PDEs · Mathematics 2019-03-01 Riccarda Rossi , Ulisse Stefanelli , Marita Thomas

The scaling laws describing the roughness development of crack surfaces are incorporated into the Griffith criterion. We show that, in the case of a Family-Vicsek scaling, the energy balance leads to a purely elastic brittle behavior. On…

Materials Science · Physics 2009-10-31 S. Morel , J. Schmittbuhl , E. Bouchaud , G. Valentin

Analytical models have been developed for fracture propagation over the last several decades and are now considered with renewed interest; the range of their applicability varies for different materials and different loading conditions.…

Materials Science · Physics 2015-09-22 D. Misseroni , A. B. Movchan , N. V. Movchan , D. Bigoni

A weak-strong uniqueness result is proved for measure-valued solutions to the system of conservation laws arising in elastodynamics. The main novelty brought forward by the present work is that the underlying stored-energy function of the…

Analysis of PDEs · Mathematics 2020-07-17 Konstantinos Koumatos , Stefano Spirito

In variational phase-field modeling of brittle fracture, the functional to be minimized is not convex, so that the necessary stationarity conditions of the functional may admit multiple solutions. The solution obtained in an actual…

Computational Engineering, Finance, and Science · Computer Science 2023-07-19 Tymofiy Gerasimov , Ulrich Römer , Jaroslav Vondřejc , Hermann G. Matthies , Laura De Lorenzis

The problem of finding what direction cracks should move is not completely solved. A commonly accepted way to predict crack directions is by computing the density of elastic potential energy stored well away from the crack tip, and finding…

Soft Condensed Matter · Physics 2009-11-10 Michael Marder

In viscoelastic materials, individually short-lived bonds collectively result in a mechanical resistance which is long-lived but finite, as ultimately cracks appear. Here we provide a microscopic mechanism by which cracks emerge from the…

Soft Condensed Matter · Physics 2018-07-04 Yuval Mulla , Giorgio Oliveri , Johannes T. B. Overvelde , Gijsje H. Koenderink

We prove the existence of solutions for an evolution quasi-variational inequality with a first order quasilinear operator and a variable convex set, which is characterized by a constraint on the absolute value of the gradient that depends…

Analysis of PDEs · Mathematics 2012-01-31 José Francisco Rodrigues , Lisa Santos

We investigate the quasi-static growth of elastic fibers in the presence of dry or viscous friction. An unusual form of destabilization beyond a critical length is described. In order to characterize this phenomenon, a new definition of…

Applied Physics · Physics 2018-06-20 Marcell G. Horváth , András Á. Sipos , Péter L. Várkonyi

We investigate numerically and theoretically the precursory intermittent activity characterizing the preliminary phase of damage accumulation prior to failure of quasi-brittle solids. We use a minimal but thermodynamically consistent model…

Statistical Mechanics · Physics 2022-03-23 Estelle Berthier , Ashwij Mayya , Laurent Ponson

Predicting the growth of large cracks in brittle materials is a fundamental unresolved problem in fracture mechanics. Under out-of-plane shear loading, an initially planar crack may fragment into multiple cracks, forming an echelon crack…

Materials Science · Physics 2026-01-07 Olivia Ward , Aditya Kumar

Slow crack growth in a model of homogenous brittle elastic material is described as a thermal activation process where stress fluctuations allow to overcome a breaking threshold through a series of irreversible steps. We study the case of a…

Statistical Mechanics · Physics 2009-11-10 S. Santucci , L. Vanel , A. Guarino , R. Scorretti , S. Ciliberto

We investigate a quasicontinuum method by means of analytical tools. More precisely, we compare a discrete-to-continuum analysis of an atomistic one-dimensional model problem with a corresponding quasicontinuum model. We consider next and…

Analysis of PDEs · Mathematics 2014-11-12 Mathias Schäffner , Anja Schlömerkemper

The problem of dynamic symmetric branching of an initial single brittle crack propagating at a given speed under plane loading conditions is studied within a continuum mechanics approach. Griffith's energy criterion and the principle of…

Materials Science · Physics 2007-05-23 E. Katzav , M. Adda-Bedia , R. Arias

A variational model to simultaneously treat Stress-Driven Rearrangement Instabilities, such as boundary discontinuities, internal cracks, external filaments, edge delamination, wetting, and brittle fractures, is introduced. The model is…

Analysis of PDEs · Mathematics 2020-06-24 Shokhrukh Yu. Kholmatov , Paolo Piovano

A quasistatic model for a horizontally loaded thin elastic composite at small strains is studied. The composite consists of two adjacent plates whose interface behaves in a cohesive fashion with respect to the slip of the two layers. We…

Analysis of PDEs · Mathematics 2023-03-13 Filippo Riva

The properties of slow crack growth in brittle materials are analyzed both theoretically and experimentally. We propose a model based on a thermally activated rupture process. Considering a 2D spring network submitted to an external load…

Materials Science · Physics 2009-11-13 Stéphane Santucci , Loic Vanel , Sergio Ciliberto

In this work, we prove that if a uniformly separated sequence in $\mathbb{R}^d$ is uniformly quasicrystalline and converges rapidly enough to a discrete set $X$ in $\mathbb{R}^d$ having the same separation radius as the sequence, then $X$…

Mathematical Physics · Physics 2025-12-24 Rodolfo Viera