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

Analysis of PDEs · Mathematics 2007-05-23 Gianni Dal Maso , Rodica Toader

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

In this paper we study the quasistatic crack growth for a cohesive zone model. We assume that the crack path is prescribed and we study the time evolution of the crack in the framework of the variational theory of rate-independent…

Analysis of PDEs · Mathematics 2007-05-23 Gianni Dal Maso , Chiara Zanini

We present the main existence result for quasistatic crack growth in the model proposed by Dal Maso, Francfort, and Toader, and prove some qualitative properties of the solutions.

Functional Analysis · Mathematics 2008-08-19 Gianni Dal Maso , Alessandro Giacomini , Marcello Ponsiglione

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

Cracks, the major vehicle for material failure, tend to accelerate to high velocities in brittle materials. In three-dimensions, cracks generically undergo a micro-branching instability at about 40% of their sonic limiting velocity. Recent…

Soft Condensed Matter · Physics 2017-12-06 Chih-Hung Chen , Eran Bouchbinder , Alain Karma

We study the atomistic-to-continuum limit for a model of a quasi-static crack evolution driven by time-dependent boundary conditions. We consider a two-dimensional atomic mass spring system whose interactions are modeled by classical…

Analysis of PDEs · Mathematics 2024-11-15 Manuel Friedrich , Joscha Seutter

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 introduce a novel constructive approach to define time evolution of critical points of an energy functional. Our procedure, which is different from other more established approaches based on viscosity approximations in infinite…

Numerical Analysis · Mathematics 2016-07-08 Marco Artina , Filippo Cagnetti , Massimo Fornasier , Francesco Solombrino

The dynamics of rapid brittle cracks is commonly studied in the framework of linear elastic fracture mechanics where nonlinearities are neglected. However, recent experimental and theoretical work demonstrated explicitly the importance of…

Materials Science · Physics 2009-11-13 Eran Bouchbinder , Ting-Shek Lo

Fracture in quasi-statically driven systems is studied by means of a discrete spring-block model. Developed from close comparison with desiccation experiments, it describes crack formation induced by friction on a substrate. The model…

Statistical Mechanics · Physics 2009-10-31 Kwan-tai Leung , Zoltan Neda

We consider the quasi-static evolution of a brittle layer on a stiff substrate; adhesion between layers is assumed to be elastic. Employing a phase-field approach we obtain the quasi-static evolution as the limit of time-discrete evolutions…

Analysis of PDEs · Mathematics 2019-10-28 Matteo Negri

We study a variant of the variational model for the quasi-static growth of brittle fractures proposed by Francfort and Marigo. The main feature of our model is that, in the discrete-time formulation, in each step we do not consider absolute…

Analysis of PDEs · Mathematics 2007-05-23 Gianni Dal Maso , Rodica Toader

In this paper we introduce a model of dynamic crack growth in viscoelastic material, where the damping term depends on the history of the deformation. The model is based on a dynamic energy dissipation balance and on a maximal dissipation…

Analysis of PDEs · Mathematics 2025-10-24 Federico Cianci

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

The problem of quasistatic evolution in small strain associative elastoplasticity is studied in the framework of the variational theory for rate-independent processes. Existence of solutions is proved through the use of incremental…

Analysis of PDEs · Mathematics 2007-05-23 Gianni Dal Maso , Antonio DeSimone , Maria Giovanna Mora

This paper focuses on rate-independent damage in elastic bodies. Since the driving energy is nonconvex, solutions may have jumps as a function of time, and in this situation it is known that the classical concept of energetic solutions for…

Analysis of PDEs · Mathematics 2014-02-06 Dorothee Knees , Riccarda Rossi , Chiara Zanini

We consider a linearly elastic body consisting of two equal symmetrically arranged layers (or half-planes) connected by a structured interface as a prospective crack path. The interface is comprised by periodic discrete system of bonds. In…

Classical Physics · Physics 2014-03-05 Gennady S. Mishuris , Leonid I. Slepyan

The interaction of crack fronts with asperities is central to the criteria of fracture in heterogeneous materials and for predicting fracture surface formation. It is known how dynamic crack fronts respond to small, 1st-order,…

Soft Condensed Matter · Physics 2025-09-17 Itamar Kolvin , Mokhtar Adda-Bedia

In this paper, we'll answer several abstract, formal questions about the nature of crack growth and nucleation. Bringing a field theory point of view to fracture illuminates things in what I hope will be an entertaining way. Formally, what…

Materials Science · Physics 2007-05-23 James P. Sethna