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Related papers: A local variational principle for fracture

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Local solutions for variational and quasi-variational inequalities are usually the best type of solutions that could practically be obtained when in case of lack of convexity or else when available numerical techniques are too limited for…

Optimization and Control · Mathematics 2024-05-16 Didier Aussel , Parin Chaipunya

Modeling important engineering problems related to flow-induced damage (in the context of hydraulic fracturing among others) depends critically on characterizing the interaction of porous media and interstitial fluid flow. This work…

Numerical Analysis · Mathematics 2012-06-27 Daniel Z. Turner

Fatigue fracture is one of the main causes of failure in structures. However, the simulation of fatigue crack growth is computationally demanding due to the large number of load cycles involved. Metals in the low cycle fatigue range often…

Computational Physics · Physics 2024-11-11 Martha Kalina , Tom Schneider , Haim Waisman , Markus Kästner

Classical molecular dynamics (MD) simulations enable modeling of materials and examination of microscopic details that are not accessible experimentally. The predictive capability of MD relies on the force field (FF) used to describe…

Phase-field fracture models are known to overestimate the crack area, a discrepancy that compromises the accuracy of fracture predictions. This issue stems from the diffuse crack representation and numerical artifacts, such as strain…

Materials Science · Physics 2026-05-06 M. Castillón , J. Segurado , I. Romero

We establish that regular flat partitions are locally minimizing for the interface energy with respect to $L^1$ perturbations of the phases. Regular flat partitions are partitions of open sets in $\mathbb{R}^2$ whose network of interfaces…

Analysis of PDEs · Mathematics 2023-02-22 Julian Fischer , Sebastian Hensel , Tim Laux , Theresa M. Simon

A crucial aspect in phase-field modeling, based on the variational formulation of brittle fracture, is the accurate representation of how the fracture surface energy is dissipated during the fracture process in the energy competition within…

Numerical Analysis · Mathematics 2025-01-29 Luigi Greco , Eleonora Maggiorelli , Matteo Negri , Alessia Patton , Alessandro Reali

In this paper a composite model for earthquake rupture initiation and propagation is proposed. The model includes aspects of damage mechanics, fiber-bundle models, and slider-block models. An array of elements is introduced in analogy to…

Geophysics · Physics 2010-07-14 G. Yakovlev , J. D. Gran , D. L. Turcotte , J. B. Rundle , W. Klein

This is the second paper of a three-part work the main aim of which is to provide a unified consistent framework for the phase-field modelling of cohesive fracture. Building on the theoretical foundations of the first paper, where…

Analysis of PDEs · Mathematics 2025-07-17 Roberto Alessi , Francesco Colasanto , Matteo Focardi

In this work, we consider adaptive mesh refinement for a monolithic phase-field description for fractures in brittle materials. Our approach is based on an a posteriori error estimator for the phase-field variational inequality realizing…

Numerical Analysis · Mathematics 2019-10-03 Katrin Mang , Mirjam Walloth , Thomas Wick , Winnifried Wollner

The principle of local covariance which was recently introduced admits a generally covariant formulation of quantum field theory. It allows a discussion of structural properties of quantum field theory as well as the perturbative…

High Energy Physics - Theory · Physics 2007-05-23 Klaus Fredenhagen

Dynamical mean-field theory (DMFT) provides an optimal local approximation for correlated lattice systems by mapping the lattice onto a self-consistent effective impurity model. To account for the missing long-range correlations, we propose…

Strongly Correlated Electrons · Physics 2026-03-04 S. D. Semenov , A. I. Lichtenstein , A. N. Rubtsov

We present a unitary framework for dissipative quantum dynamics that can be efficiently applied to large-scale Fermi systems. The method introduces local Hermitian operators that emulate frictional forces while strictly preserving the…

Nuclear Theory · Physics 2025-12-16 J. E. Alba-Arroyo , Daniel Pęcak , Michael McNeil Forbes , Gabriel Wlazłowski

The purpose of this article is to review the developments related to the notion of local fractional derivative introduced in 1996. We consider its definition, properties, implications and possible applications. This involves the local…

Chaotic Dynamics · Physics 2018-05-22 Kiran M. Kolwankar

Fracture mechanics is crucial for many fields of engineering, as precisely predicting failure of structures and parts is required for efficient designs. The simulation of failure processes is, from a mechanical and a numerical point of…

Materials Science · Physics 2022-06-15 Sebastian Pech , Markus Lukacevic , Josef Füssl

We present a generalization of the variational principle that is compatible with any Hamiltonian eigenstate that can be specified uniquely by a list of properties. This variational principle appears to be compatible with a wide range of…

Chemical Physics · Physics 2020-02-07 Jacqueline A. R. Shea , Elise Gwin , Eric Neuscamman

In this study, we analyze the flow filtration process of slightly compressible fluids in fractured porous media. We model the coupled fractured porous media system, where the linear Darcy flow is considered in porous media and the nonlinear…

Analysis of PDEs · Mathematics 2022-05-30 Pushpi J. Paranamana , Eugenio Aulisa , Akif Ibragimov , Magdalena Toda

Phase field theory for fracture is developed at large strains with an emphasis on a correct introduction of surface stresses. This is achieved by multiplying the cohesion and gradient energies by the local ratio of the crack surface areas…

Applied Physics · Physics 2020-11-30 Hossein Jafarzadeh , Gholam Hossein Farrahi , Valery I. Levitas , Mahdi Javanbakht

We propose a new direction-dependent model for the unilateral constraint involved in the phase field approach to fracture and also in the continuous damage mechanics models. The construction of this phase field model is informed by…

Computational Engineering, Finance, and Science · Computer Science 2023-10-05 Yangyuanchen Liu , Cheng Cheng , Vahid Ziaei-Rad , Yongxing Shen

We develop worldline formulations of covariant fracton gauge theories. These are a one-parameter family of gauge theories of a rank-two symmetric tensor field, invariant under a scalar gauge transformation involving a double derivative.…

High Energy Physics - Theory · Physics 2026-02-10 Filippo Fecit , Davide Rovere