Open Access
A Continuum Phase Field Model for Fracture
Ralf Müller,Charlotte Kuhn +1 more
TLDR
A variational free-discontinuity formulation of brittle fracture was given by Francfort and Marigo as discussed by the authors, where the total energy is minimized with respect to the crackgeometry and the displacement field simultaneously.Abstract:
A variational free-discontinuity formulation of brittle fracture was given by Francfortand Marigo [1], where the total energy is minimized with respect to the crackgeometry and the displacement field simultaneously. The entire evolution of cracksincluding their initiation and branching is determined by this minimization principlerequiring no further criterion. However, a direct numerical discretization of themodel faces considerable difficulties as the displacement field is discontinuous inthe presence of cracks.read more
Citations
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Dissertation
On the theory of superconductivity
TL;DR: In this article, it was shown that a metal should be superconductive if a set of corners of a Brillouin zone is lying very near the Fermi surface, considered as a sphere, which limits the region in the momentum space completely filled with electrons.
Journal ArticleDOI
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.
Journal ArticleDOI
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.
Journal ArticleDOI
A unified phase-field theory for the mechanics of damage and quasi-brittle failure
TL;DR: In this paper, a unified phase-field theory for the mechanics of damage and quasi-brittle failure is proposed within the framework of thermodynamics, where the crack phase field and its gradient are introduced to regularize the sharp crack topology in a purely geometric context.
Journal ArticleDOI
Phase field modeling of fracture in multi-physics problems. Part I. Balance of crack surface and failure criteria for brittle crack propagation in thermo-elastic solids
TL;DR: In this paper, a generalization of recently developed continuum phase field models for brittle fracture towards fully coupled thermo-mechanical and multi-physics problems at large strains is presented.
References
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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.
Journal ArticleDOI
A Path Independent Integral and the Approximate Analysis of Strain Concentration by Notches and Cracks
TL;DR: In this paper, an integral is exhibited which has the same value for all paths surrounding a class of notches in two-dimensional deformation fields of linear or non-linear elastic materials.
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.
Dissertation
On the theory of superconductivity
TL;DR: In this article, it was shown that a metal should be superconductive if a set of corners of a Brillouin zone is lying very near the Fermi surface, considered as a sphere, which limits the region in the momentum space completely filled with electrons.
Book
The Variational Approach to Fracture
TL;DR: In this article, a weak variational evolution is proposed for 1D traction on a fiber reinforced matrix, and a variational formulation for fatigue is presented, which is based on the soft belly of Griffith's formulation.