An explicit residual-type error estimator for Q1-quadrilateral extended finite element method in two-dimensional linear elastic fracture mechanics

2012 ◽  
Vol 90 (9) ◽  
pp. 1118-1155 ◽  
Author(s):  
T. Gerasimov ◽  
M. Rüter ◽  
E. Stein
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Fracture Mechanics ◽  
Extended Finite Element Method ◽  
Linear Elastic Fracture Mechanics ◽  
Error Estimator ◽  
Two Dimensional ◽  
Extended Finite Element ◽  
Linear Elastic ◽  
Elastic Fracture

Application of the Finite Element Method to Linear Elastic Fracture Mechanics

1991 ◽  
Vol 44 (10) ◽  
pp. 447-461 ◽  
Author(s):  
Leslie Banks-Sills
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stress Intensity ◽  
Fracture Mechanics ◽  
Displacement Field ◽  
Three Dimensional ◽  
Linear Elastic Fracture Mechanics ◽  
The Finite Element Method ◽  
Linear Elastic ◽  
Elastic Fracture

Use of the finite element method to treat two and three-dimensional linear elastic fracture mechanics problems is becoming common place. In general, the behavior of the displacement field in ordinary elements is at most quadratic or cubic, so that the stress field is at most linear or quadratic. On the other hand, the stresses in the neighborhood of a crack tip in a linear elastic material have been shown to be square root singular. Hence, the problem begins by properly modeling the stresses in the region adjacent to the crack tip with finite elements. To this end, quarter-point, singular, isoparametric elements may be employed; these will be discussed in detail. After that difficulty has been overcome, the stress intensity factor must be extracted from either the stress or displacement field or by an energy based method. Three methods are described here: displacement extrapolation, the stiffness derivative and the area and volume J-integrals. Special attention will be given to the virtual crack extension which is employed by the latter two methods. A methodology for calculating stress intensity factors in two and three-dimensional bodies will be recommended.

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.

A gradient weighted extended finite element method (GW-XFEM) for fracture mechanics

2019 ◽  
Vol 230 (7) ◽  
pp. 2385-2398 ◽  
Author(s):  
S. Z. Feng ◽  
S. P. A. Bordas ◽  
X. Han ◽  
G. Wang ◽  
Z. X. Li
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Fracture Mechanics ◽  
Extended Finite Element Method ◽  
Extended Finite Element ◽  
Element Method
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