Journal ArticleDOI
Modified Newton methods for solving fully monolithic phase-field quasi-static brittle fracture propagation
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TLDR
In this article, a modified Newton solver for phase-field fracture propagation with Jacobian matrix modification is presented, which switches smoothly between full Newton and Newton-like steps to solve the nonlinear flow problem.About:
This article is published in Computer Methods in Applied Mechanics and Engineering.The article was published on 2017-10-01. It has received 120 citations till now. The article focuses on the topics: Quasi-Newton method & Newton's method in optimization.read more
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Book ChapterDOI
Phase-field modeling of fracture
TL;DR: This chapter provides an extensive overview of the literature on the so-called phase-field fracture/damage models (PFMs), particularly, for quasi-static and dynamic fracture of brittle and quasi-brittle materials, from the points of view of a computational mechanician.
Journal ArticleDOI
Phase-field modeling of fluid-driven dynamic cracking in porous media
TL;DR: In this article, a phase field model for fluid-driven dynamic crack propagation in poroelastic media is proposed and verified through three classical benchmark problems which are compared to analytical solutions for dynamic consolidation and pressure distribution in a single crack and in a specimen with two sets of joints.
Journal ArticleDOI
On the BFGS monolithic algorithm for the unified phase field damage theory
TL;DR: This work proposes in this work, for the first time, to use the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm to solve in a monolithic manner the system of coupled governing equations, rather than the standard Newton one which is notoriously poor for problems involving non-convex energy functional.
Journal ArticleDOI
Phase field fracture modelling using quasi-Newton methods and a new adaptive step scheme
TL;DR: In this paper, the authors investigate the potential of quasi-Newton methods in facilitating convergence of monolithic solution schemes for phase field fracture modelling, and propose a new adaptive time increment scheme to further reduce the computational cost while allowing to accurately resolve sudden changes in material behavior.
Journal ArticleDOI
A modified Gurson-type plasticity model at finite strains: formulation, numerical analysis and phase-field coupling
TL;DR: In this article, the authors developed a new theoretical and computational framework for the phase field modeling of ductile fracture in conventional elastic-plastic solids under finite strain deformation.
References
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Book
Numerical Optimization
Jorge Nocedal,Stephen J. Wright +1 more
TL;DR: Numerical Optimization presents a comprehensive and up-to-date description of the most effective methods in continuous optimization, responding to the growing interest in optimization in engineering, science, and business by focusing on the methods that are best suited to practical problems.
Journal ArticleDOI
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.
Book
Finite Element Method for Elliptic Problems
TL;DR: In this article, Ciarlet presents a self-contained book on finite element methods for analysis and functional analysis, particularly Hilbert spaces, Sobolev spaces, and differential calculus in normed vector spaces.
Journal ArticleDOI
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.
Journal ArticleDOI
A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits
TL;DR: 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.