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
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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.About:
This article is published in Computer Methods in Applied Mechanics and Engineering.The article was published on 2015-09-01. It has received 416 citations till now. The article focuses on the topics: Crack closure & Crack growth resistance curve.read more
Citations
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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 II. Coupled Brittle-to-Ductile Failure Criteria and Crack Propagation in Thermo-Elastic-Plastic Solids
TL;DR: In this article, a generalization of recently developed continuum phase field models from brittle to ductile fracture coupled with thermo-plasticity at finite strains is presented, which uses a geometric approach to the diffusive crack modeling based on the introduction of a balance equation for a regularized crack surface.
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A phase-field formulation for fracture in ductile materials: Finite deformation balance law derivation, plastic degradation, and stress triaxiality effects
TL;DR: In this paper, a cubic degradation function was proposed to provide a stress-strain response prior to crack initiation, which more closely approximates linear elastic behavior, and a derivation of the governing equations in terms of a general energy potential from balance laws that describe the kinematics of both the body and phase-field.
A Continuum Phase Field Model for Fracture
Ralf Müller,Charlotte Kuhn +1 more
TL;DR: 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.
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A length scale insensitive phase-field damage model for brittle fracture
Jian-Ying Wu,Vinh Phu Nguyen +1 more
TL;DR: In this article, a phase-field regularized cohesive zone model (CZM) with linear softening law is applied to brittle fracture. But the model is not suitable for the case of nonlinear singularities (e.g., corners, notches, etc.).
References
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Journal ArticleDOI
A finite element method for crack growth without remeshing
TL;DR: In this article, a displacement-based approximation is enriched near a crack by incorporating both discontinuous elds and the near tip asymptotic elds through a partition of unity method.
Book
Maximum principles in differential equations
TL;DR: The One-Dimensional Maximum Principle (MDP) as mentioned in this paper is a generalization of the one-dimensional maximum principle (OMP) for the construction of hyperbolic equations.
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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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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.