Journal ArticleDOI
A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits
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TLDR
In this paper, a variational framework for rate-independent diffusive fracture was proposed based on the introduction of a local history field, which contains a maximum reference energy obtained in the deformation history, which may be considered as a measure for the maximum tensile strain obtained in history.About:
This article is published in Computer Methods in Applied Mechanics and Engineering.The article was published on 2010-11-15. It has received 1702 citations till now. The article focuses on the topics: Fracture mechanics & Phase field models.read more
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A phase-field description of dynamic brittle fracture
TL;DR: It is shown that the combination of the phase-field model and local adaptive refinement provides an effective method for simulating fracture in three dimensions.
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A review on phase-field models of brittle fracture and a new fast hybrid formulation
TL;DR: In this article, the authors provide an overview of the existing quasi-static and dynamic phase-field fracture formulations from the physics and the mechanics communities, and propose and test the so-called hybrid formulation, which leads within a staggered implementation to an incrementally linear problem.
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An energy approach to the solution of partial differential equations in computational mechanics via machine learning: Concepts, implementation and applications
Esteban Samaniego,Cosmin Anitescu,Somdatta Goswami,Vien Minh Nguyen-Thanh,Hongwei Guo,Khader M. Hamdia,Xiaoying Zhuang,Timon Rabczuk +7 more
TL;DR: This contribution focuses in mechanical problems and analyze the energetic format of the PDE, where the energy of a mechanical system seems to be the natural loss function for a machine learning method to approach a mechanical problem.
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Phase-field modeling of ductile fracture
TL;DR: In this article, a phase-field model for ductile fracture of elasto-plastic solids in the quasi-static kinematically linear regime is proposed, which captures the entire range of behavior of a ductile material exhibiting $$J_2$$J2-PLasticity, encompassing plasticization, crack initiation, propagation and failure.
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A higher-order phase-field model for brittle fracture: Formulation and analysis within the isogeometric analysis framework
TL;DR: This work derives the thermodynamically consistent governing equations for the fourth-order phase-field model by way of a variational principle based on energy balance assumptions, which leads to higher regularity in the exact phase- field solution, which can be exploited by the smooth spline function spaces utilized in isogeometric analysis.
References
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The Phenomena of Rupture and Flow in Solids
TL;DR: In this article, the authors investigated the effect of surface scratches on the mechanical strength of solids, and some general conclusions were reached which appear to have a direct bearing on the problem of rupture, from an engineering standpoint, and also on the larger question of the nature of intermolecular cohesion.
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Optimal approximations by piecewise smooth functions and associated variational problems
David Mumford,Jayant Shah +1 more
TL;DR: In this article, the authors introduce and study the most basic properties of three new variational problems which are suggested by applications to computer vision, and study their application in computer vision.
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Revisiting brittle fracture as an energy minimization problem
TL;DR: In this paper, a variational model of quasistatic crack evolution is proposed, which frees itself of the usual constraints of that theory : a preexisting crack and a well-defined crack path.
Book
An Introduction to Γ-Convergence
TL;DR: In this article, the authors present a characterization of the topology of convergences in the calculus of variations with respect to the following properties: 1. Minimum problems for integral functionals. 2. Relaxation.
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Numerical experiments in revisited brittle fracture
TL;DR: The numerical implementation of the model of brittle fracture developed in Francfort and Marigo (1998) is presented in this paper, where various computational methods based on variational approximations of the original functional are proposed.