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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

The classical variational phase-field model for brittle fracture effectively predicts the growth of large pre-existing cracks. However, the modeling of crack nucleation continues to be a significant challenge. Crack nucleation under uniform…

Materials Science · Physics 2025-02-10 Umar Khayaz , Aarosh Dahal , Aditya Kumar

This paper presents a computational framework for quasi-static brittle fracture in three dimensional solids. The paper set outs the theoretical basis for determining the initiation and direction of propagating cracks based on the concept of…

Computational Physics · Physics 2013-12-02 Lukasz Kaczmarczyk , Mohaddeseh Mousavi Nezhad , Chris Pearce

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

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

We study an approximation scheme for a variational theory of quasi-static crack growth based on an eigendeformation approach. We consider a family of energy functionals depending on a small parameter $\varepsilon$ and on two fields, the…

Analysis of PDEs · Mathematics 2026-02-13 Ba Duc Duong , Manuel Friedrich

We propose a variational phase-field model of fracture capable of accounting for arbitrary closed convex strength domains. Unlike traditional models based on Ambrosio and Tortorelli regularization, the phase-field variable does not affect…

Applied Physics · Physics 2025-07-01 Blaise Bourdin , Jean-Jacques Marigo , Corrado Maurini , Camilla Zolesi

This paper presents a formulation for brittle fracture in 3D elastic solids within the context of configurational mechanics. The local form of the first law of thermodynamics provides a condition for equilibrium of the crack front. The…

Computational Engineering, Finance, and Science · Computer Science 2017-08-02 Lukasz Kaczmarczyk , Zahur Ullah , Chris J. Pearce

The purpose of this paper is to fill the gap between the classical treatment of brittle fracture mechanics and the new idea of considering the crack evolution as a free discontinuity problem. Griffith and Irwin criterions of crack…

Analysis of PDEs · Mathematics 2007-05-23 Marius Buliga

Variational phase-field models of brittle fracture are powerful tools for studying Griffith-type crack propagation in complex scenarios. However, as approximations of Griffith's theory-which does not incorporate a strength criterion-these…

Applied Physics · Physics 2026-01-06 Francesco Vicentini , Jonas Heinzmann , Pietro Carrara , Laura De Lorenzis

We present a new data-driven paradigm for variational brittle fracture mechanics. The fracture-related material modeling assumptions are removed and the governing equations stemming from variational principles are combined with a set of…

Computational Engineering, Finance, and Science · Computer Science 2020-09-11 Pietro Carrara , Laura De Lorenzis , Laurent Stainier , Michael Ortiz

This work addresses an efficient Global-Local approach supplemented with predictor-corrector adaptivity applied to anisotropic phase-field brittle fracture. The phase-field formulation is used to resolve the sharp crack surface topology on…

Numerical Analysis · Mathematics 2020-02-19 Nima Noii , Fadi Aldakheel , Thomas Wick , Peter Wriggers

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

In a recent contribution, Kumar, Bourdin, Francfort, and Lopez-Pamies (J. Mech. Phys. Solids 142:104027, 2020) have introduced a comprehensive macroscopic phase-field theory for the nucleation and propagation of fracture in linear elastic…

Materials Science · Physics 2022-07-21 Aditya Kumar , K. Ravi-Chandar , Oscar Lopez-Pamies

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 variational approach to fracture is effective for simulating the nucleation and propagation of complex crack patterns, but is computationally demanding. The model is a strongly nonlinear non-convex variational inequality that demands…

Numerical Analysis · Mathematics 2016-05-18 Patrick E. Farrell , Corrado Maurini

With the fundamental objective of establishing the universality of the Griffith energy competition to describe the growth of large cracks in solids \emph{not} just under monotonic but under general loading conditions, this paper puts forth…

Other Condensed Matter · Physics 2024-04-23 Subhrangsu Saha , John E. Dolbow , Oscar Lopez-Pamies

A nonlocal field theory of peridynamic type is applied to model the brittle fracture problem. The elastic fields obtained from the nonlocal model are shown to converge in the limit of vanishing non-locality to solutions of classic plane…

Analysis of PDEs · Mathematics 2020-07-21 Robert P. Lipton , Prashant K. Jha

The phase-field model for fracture, despite its popularity and ease of implementation comes with its set of computational challenges. They are the non-convex energy functional, variational inequality due to fracture irreversibility, the…

Numerical Analysis · Mathematics 2022-06-24 Ritukesh Bharali , Fredrik Larsson , Ralf Jänicke

Over the past seven years, full-field analyses of a wide range of classical as well as modern quasi-static fracture experiments on nominally elastic brittle materials -- ranging from hard ceramics to soft elastomers -- have repeatedly…

Materials Science · Physics 2024-11-26 Yangyuanchen Liu , Oscar Lopez-Pamies , John E. Dolbow
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