Preconditioning strategies for vectorial finite element linear systems arising from phase-field models for fracture mechanics

2021 ◽  
Vol 373 ◽  
pp. 113472
Author(s):  
M.A. Badri ◽  
G. Rastiello ◽  
E. Foerster
Keyword(s):  
Finite Element ◽  
Fracture Mechanics ◽  
Linear Systems ◽  
Phase Field ◽  
Phase Field Models

scholarly journals Discrete and Phase Field Methods for Linear Elastic Fracture Mechanics: A Comparative Study and State-of-the-Art Review

2019 ◽  
Vol 9 (12) ◽  
pp. 2436 ◽  
Author(s):  
Adrian Egger ◽  
Udit Pillai ◽  
Konstantinos Agathos ◽  
Emmanouil Kakouris ◽  
Eleni Chatzi ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Fracture Mechanics ◽  
Phase Field ◽  
Linear Elastic Fracture Mechanics ◽  
Field Methods ◽  
Linear Elastic ◽  
Elastic Fracture ◽  
Phase Field Methods ◽  
Element Method

Three alternative approaches, namely the extended/generalized finite element method (XFEM/GFEM), the scaled boundary finite element method (SBFEM) and phase field methods, are surveyed and compared in the context of linear elastic fracture mechanics (LEFM). The purpose of the study is to provide a critical literature review, emphasizing on the mathematical, conceptual and implementation particularities that lead to the specific advantages and disadvantages of each method, as well as to offer numerical examples that help illustrate these features.

scholarly journals Non-conforming multipatches for NURBS-based finite element analysis of higher-order phase-field models for brittle fracture

2020 ◽  
Vol 235 ◽  
pp. 107133
Author(s):  
Khuong D. Nguyen ◽  
Charles E.Augarde ◽  
William M. Coombs ◽  
H. Nguyen-Xuan ◽  
M. Abdel-Wahab
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Brittle Fracture ◽  
Phase Field ◽  
Higher Order ◽  
Element Analysis ◽  
Phase Field Models

scholarly journals An assessment of phase field fracture: crack initiation and growth

2021 ◽  
Vol 379 (2203) ◽  
pp. 20210021 ◽  
Author(s):  
Philip K. Kristensen ◽  
Christian F. Niordson ◽  
Emilio Martínez-Pañeda
Keyword(s):  
Finite Element ◽  
Fracture Mechanics ◽  
Phase Field ◽  
Ad Hoc ◽  
Stable Crack Propagation ◽  
Variational Structure ◽  
Fracture Crack ◽  
Fracture Models ◽  
Material Length Scale ◽  
Material Length

The phase field paradigm, in combination with a suitable variational structure, has opened a path for using Griffith’s energy balance to predict the fracture of solids. These so-called phase field fracture methods have gained significant popularity over the past decade, and are now part of commercial finite element packages and engineering fitness- for-service assessments. Crack paths can be predicted, in arbitrary geometries and dimensions, based on a global energy minimization—without the need for ad hoc criteria. In this work, we review the fundamentals of phase field fracture methods and examine their capabilities in delivering predictions in agreement with the classical fracture mechanics theory pioneered by Griffith. The two most widely used phase field fracture models are implemented in the context of the finite element method, and several paradigmatic boundary value problems are addressed to gain insight into their predictive abilities across all cracking stages; both the initiation of growth and stable crack propagation are investigated. In addition, we examine the effectiveness of phase field models with an internal material length scale in capturing size effects and the transition flaw size concept. Our results show that phase field fracture methods satisfactorily approximate classical fracture mechanics predictions and can also reconcile stress and toughness criteria for fracture. The accuracy of the approximation is however dependent on modelling and constitutive choices; we provide a rationale for these differences and identify suitable approaches for delivering phase field fracture predictions that are in good agreement with well-established fracture mechanics paradigms. This article is part of a discussion meeting issue ‘A cracking approach to inventing new tough materials: fracture stranger than friction’.

Efficient and reliable finite element techniques for phase field models

2010 ◽  
Vol 101 (4) ◽  
pp. 498-502
Author(s):  
Marcus Stiemer ◽  
André Große-Wöhrmann ◽  
Slawa Gladkov ◽  
Bob Svendsen ◽  
Robert Spatschek ◽  
...  
Keyword(s):  
Finite Element ◽  
Phase Field ◽  
Phase Field Models

scholarly journals Discussion of hardening effects on phase field models for fracture

2021 ◽  
Vol 349 ◽  
pp. 02001
Author(s):  
Aris Tsakmakis ◽  
Michael Vormwald
Keyword(s):  
Fracture Mechanics ◽  
Phase Field ◽  
Fatigue Cracks ◽  
Brittle Materials ◽  
Additional Term ◽  
Field Method ◽  
Systematic Investigation ◽  
Phase Field Method ◽  
Isotropic Hardening ◽  
Phase Field Models

Phase field models have been successfully applied in recent years to a variety of fracture mechanics problems, such as quasi-brittle materials, dynamic fracture mechanics, fatigue cracks in brittle materials, as well as ductile materials. The basic idea of the method is to introduce an additional term in the energy functional describing the state of material bodies. A new state variable is included in this term, the so-called phase field, and enables to determine the surface energy of the crack. This approach allows to model phenomena such as crack initiation, crack branching and buckling of cracks, as well as the modelling of the crack front in three-dimensional geometries, without further assumptions. There is yet no systematic investigation of the influence of strain hardening on crack development within the phase field method. Thus, the aim of the paper is to provide an analysis of the effect of kinematic and isotropic hardening on the evolution of the phase field variable.

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