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We give an alternative proof of the regularity, up to the loose end, of minimizers, resp. critical points of the Mumford-Shah functional when they are sufficiently close to the cracktip, resp. they consist of a single arc terminating at an…

Analysis of PDEs · Mathematics 2021-10-19 Camillo De Lellis , Matteo Focardi , Silvia Ghinassi

In this letter we address the fragmentation of thin, brittle layers due to the impact of high-velocity projectiles. Our approach is a geometric statistical one, with lines and circles playing the role of cracks, randomly distributed over…

Soft Condensed Matter · Physics 2014-09-30 Rebeca C. Falcão , Fernando Parisio

This paper is concerned with the asymptotic analysis of a sequence of variational models of brittle damage in the context of linearized elasticity in the two-dimensional discrete setting. We consider a discrete version of Francfort and…

Analysis of PDEs · Mathematics 2025-02-13 Elise Bonhomme

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

Molecular-dynamics simulations of fracture in metallic glass-like systems are observed to undergo embrittlement due to a small change in interatomic potential. This change in fracture toughness, however, is not accompanied by a…

Materials Science · Physics 2009-10-31 M. L. Falk

We consider regularity of the crack set associated to a minimizer of the Griffith fracture energy, often used in modeling brittle materials. We show that the crack is uniformly rectifiable which in conjunction with our previous…

Analysis of PDEs · Mathematics 2025-10-13 Manuel Friedrich , Camille Labourie , Kerrek Stinson

We study a planar thin brittle beam subject to elastic deformations and cracks described in terms of a nonlinear Griffith energy functional acting on $SBV$ deformations of the beam. In particular we consider the case in which elastic bulk…

Analysis of PDEs · Mathematics 2016-02-25 Bernd Schmidt

The failure of brittle solids involves, before macroscopic rupture, power-law distributed avalanches of local rupture events whereby microcracks nucleate and grow, which are also observed in for an elastic interface evolving in a…

Soft Condensed Matter · Physics 2019-03-01 Vincent Démery , Véronique Dansereau , Estelle Berthier , Laurent Ponson , Jérôme Weiss

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

In chemically reactive environments, the mechanical integrity of geomaterials is fundamentally compromised by solid matrix dissolution. In this study, we propose a fully coupled chemo-mechanical phase-field framework to capture the dynamic…

Materials Science · Physics 2026-04-14 Fanyu Wu , Chong Liu , Manolis Veveakis , Manman Hu

A phase-field description of brittle fracture is employed in the reported four-point bending analyses of monolithic and laminated glass plates. Our aims are: (i) to compare different phase-field fracture formulations applied to thin glass…

Computational Engineering, Finance, and Science · Computer Science 2020-12-30 Jaroslav Schmidt , Alena Zemanová , Jan Zeman , Michal Šejnoha

This paper is the first part of an ongoing project aimed at providing a local minimality criterion, based on a second variation approach, for the triple point configurations of the Mumford-Shah functional.

Analysis of PDEs · Mathematics 2017-02-08 Riccardo Cristoferi

Cracks are created by massive breakage of molecular or atomic bonds. The latter, in its turn, leads to the highly localized loss of material, which is the reason why even closed cracks are visible by a naked eye. Thus, fracture can be…

Materials Science · Physics 2016-10-28 Konstantin Volokh

This paper presents a framework for modeling failure in quasi-brittle geomaterials under different loading conditions. A micromechanics-based model is proposed in which the field variables are linked to physical mechanisms at the microcrack…

Materials Science · Physics 2021-11-12 Jacinto Ulloa , Jef Wambacq , Roberto Alessi , Esteban Samaniego , Geert Degrande , Stijn François

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 present a unified theory of fracture in disordered brittle media that reconciles apparently conflicting results reported in the literature. Our renormalization group based approach yields a phase diagram in which the percolation fixed…

Statistical Mechanics · Physics 2013-05-09 Ashivni Shekhawat , Stefano Zapperi , James P. Sethna

We derive sharp-interface models for one-dimensional brittle fracture via the inverse-deformation approach. Methods of Gamma-convergence are employed to obtain the singular limits of previously proposed models. The latter feature a local,…

Analysis of PDEs · Mathematics 2024-03-05 Timothy J. Healey , Roberto Paroni , Phoebus Rosakis

A new algorithm to determine the position of the crack (discontinuity set) of certain minimizers of Mumford-Shah functional in situations when a crack-tip occurs is introduced. The conformal mapping $w=\sqrt{z}$ in the complex plane is used…

Numerical Analysis · Mathematics 2015-11-25 Zhilin Li , Hayk Mikayelyan

Soft-walled microchannels arise in many applications, ranging from organ-on-a-chip platforms to soft-robotic actuators. However, despite extensive research on their static and dynamic response, the potential failure of these devices has not…

Computational Engineering, Finance, and Science · Computer Science 2026-03-17 Ziyu Wang , Ivan C. Christov

This study introduces a physics-based machine learning framework for modeling both brittle and ductile fractures. Unlike physics-informed neural networks, which solve partial differential equations by embedding physical laws as soft…

Numerical Analysis · Mathematics 2025-02-14 Fadi Aldakheel , Elsayed S. Elsayed , Yousef Heider , Oliver Weeger