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

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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

In this paper we focus on the finite-dimensional approximation of quasi-static evolutions of critical points of the phase-field model of brittle fracture. In a space discretized setting, we first discuss an alternating minimization scheme…

Numerical Analysis · Mathematics 2019-03-07 Stefano Almi , Sandro Belz

We define a notion of quasi-static evolution for the elliptic approximation of the Mumford-Shah functional proposed by Ambrosio and Tortorelli. Then we prove that this regular evolution converges to a quasi-static growth of brittle…

Analysis of PDEs · Mathematics 2007-05-23 Alessandro Giacomini

We introduce a new model of irreversible quasistatic crack growth in which the evolution of cracks is the limit of a suitably modified $\epsilon$-gradient flow of the energy functional, as the "viscosity" parameter $\epsilon$ tends to zero.

Analysis of PDEs · Mathematics 2007-05-23 Rodica Toader , Chiara Zanini

We argue that nucleation of brittle cracks in initially flawless soft elastic solids is preceded by a nonlinear elastic instability, which cannot be captured without accounting for geometrical precise description of finite elastic…

Soft Condensed Matter · Physics 2024-06-17 D. Riccobelli , P. Ciarletta , G. Vitale , C. Maurini , L. Truskinovsky

We generalize lattice models of brittle fracture to arbitrary nonlinear force laws and study the existence of arrested semi-infinite cracks. Unlike what is seen in the discontinuous case studied to date, the range in driving displacement…

Soft Condensed Matter · Physics 2009-10-31 David A. Kessler , Herbert Levine

We study how the loading rate, specimen geometry and microstructural texture select the dynamics of a crack moving through an heterogeneous elastic material in the quasi-static approximation. We find a transition, fully controlled by two…

Statistical Mechanics · Physics 2013-09-23 Jonathan Barés , Luc Barbier , Daniel Bonamy

We study a class of models for brittle fracture: elastic theory models which allow for cracks but not for plastic flow. We show that these models exhibit, at all finite temperatures, a transition to fracture under applied load similar to…

Materials Science · Physics 2009-10-28 Alex Buchel , James P. Sethna

We consider load controlled quasistatic evolution. Well posedness results for the nonlocal continuum model related to peridynamics are established. We show local existence and uniqueness of quasistatic evolution for load paths originating…

Analysis of PDEs · Mathematics 2023-01-04 Debdeep Bhattacharya , Robert P. Lipton

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

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 paper we propose a notion of irreversibility for the evolution of cracks in presence of cohesive forces, which allows for different responses in the loading and unloading processes, motivated by a variational approximation with…

Analysis of PDEs · Mathematics 2020-12-30 Marco Bonacini , Sergio Conti , Flaviana Iurlano

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

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

Visco-energetic solutions have been recently advanced as a new solution concept for rate-independent systems, alternative to energetic solutions/quasistatic evolutions and balanced viscosity solutions. In the spirit of this novel concept,…

Analysis of PDEs · Mathematics 2022-05-18 Gianni Dal Maso , Riccarda Rossi , Giuseppe Savaré , Rodica Toader

Quasi-brittle behavior where macroscopic failure is preceded by stable damaging and intensive cracking activity is a desired feature of materials because it makes fracture predictable. Based on a fiber bundle model with global load sharing…

Materials Science · Physics 2016-04-07 Ehud D. Karpas , Ferenc Kun

Dynamic fracture experiments were performed in PMMA over a wide range of velocities and reveal that the fracture energy exhibits an abrupt 3-folds increase from its value at crack initiation at a well-defined critical velocity, below the…

Classical Physics · Physics 2010-02-15 Julien Scheibert , Claudia Guerra , Fabrice Célarié , Davy Dalmas , Daniel Bonamy

Fracture involves interaction across large and small length scales. With the application of enough stress or strain to a brittle material, atomistic scale bonds will break, leading to fracture of the macroscopic specimen. From the…

Soft Condensed Matter · Physics 2022-02-04 Debdeep Bhattacharya , Patrick Diehl , Robert P. Lipton

A field theory is presented for predicting damage and fracture in quasi-brittle materials. The approach taken here is new and blends a non-local constitutive law with a two-point phase field. In this formulation, the material displacement…

Materials Science · Physics 2025-10-07 Semsi Coskun , Davood Damircheli , 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