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Related papers: Quasistatic fracture evolution

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We present a numerical implementation of a model of quasi-static crack growth in linearly elastic-perfectly plastic materials. We assume that the displacement is antiplane, and that the cracks and the plastic slips are localized on a…

Numerical Analysis · Mathematics 2021-11-18 Gianni Dal Maso , Luca Heltai

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

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

Quasistatic evolutions of critical points of time-dependent energies exhibit piecewise smooth behavior, making them useful for modeling continuum mechanics phenomena like elastic-plasticity and fracture. Traditionally, such evolutions have…

Optimization and Control · Mathematics 2026-01-09 Stefano Almi , Massimo Fornasier , Jona Klemenc , Alessandro Scagliotti

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

A mechanical model is introduced for predicting the initiation and evolution of complex fracture patterns without the need for a damage variable or law. The model, a continuum variant of Newton's second law, uses integral rather than…

Analysis of PDEs · Mathematics 2016-02-02 Robert Lipton , Stewart Silling , Richard Lehoucq

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

The dynamics of a single crack moving through a heterogeneous medium is studied in the quasi-static approximation. Equations of motion for the crack front are formulated and the resulting scaling behaviour analyzed. In a model scalar system…

Disordered Systems and Neural Networks · Physics 2009-10-28 Sharad Ramanathan , Deniz Ertaş , Daniel S. Fisher

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

In this work, we study the finite difference approximation for a class of nonlocal fracture models. The nonlocal model is initially elastic but beyond a critical strain the material softens with increasing strain. This model is formulated…

Numerical Analysis · Mathematics 2019-05-01 Prashant K. Jha , Robert Lipton

The enforcement of global energy conservation in phase-field fracture simulations has been an open problem for the last 25 years. Specifically, the occurrence of unstable fracture is accompanied by a loss in total potential energy, which…

Materials Science · Physics 2026-01-01 Juan Michael Sargado , Joachim Mathiesen

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

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

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

We provide an adaptive finite element approximation for a model of quasi-static crack growth in dimension two. The discrete setting consists of integral functionals that are defined on continuous, piecewise affine functions, where the…

Analysis of PDEs · Mathematics 2025-03-25 Vito Crismale , Manuel Friedrich , Joscha Seutter

A nonlocal model of peridynamic type for dynamic brittle damage is introduced consisting of two phases, one elastic and the other inelastic. Evolution from the elastic to the inelastic phase depends on material strength. Existence and…

Analysis of PDEs · Mathematics 2024-04-02 Robert P. Lipton , Debdeep Bhattacharya

We study a relaxed formulation of the quasistatic evolution problem in the context of small strain associative elastoplasticity with softening. The relaxation takes place in spaces of generalized Young measures. The notion of solution is…

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

Crack propagation is studied in a two dimensional decagonal model quasicrystal. The simulations reveal the dominating role of highly coordinated atomic environments as structure intrinsic obstacles for both dislocation motion and crack…

Materials Science · Physics 2009-10-31 R. Mikulla , J. Stadler , F. Krul , H. -R. Trebin , P. Gumbsch

Shear cracks propagation is a basic dynamical process that mediates interfacial failure. We develop a general weakly nonlinear elastic theory of shear cracks and show that these experience tensile-mode crack tip deformation, including…

Materials Science · Physics 2015-06-03 Roi Harpaz , Eran Bouchbinder

Superficial (two dimensional) crack patterns appear when a thin layer of material elastically attached to a substrate contracts. We study numerically the maturation process undergone by these crack patterns when they are allowed to adapt in…

Statistical Mechanics · Physics 2009-11-10 E. A. Jagla