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.

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.

Update: Application of the Finite Element Method to Linear Elastic Fracture Mechanics

2010 ◽  
Vol 63 (2) ◽  
Author(s):  
Leslie Banks-Sills
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Linear Elastic Fracture Mechanics ◽  
The Finite Element Method ◽  
Intensity Factors ◽  
Linear Elastic ◽  
Elastic Fracture ◽  
Element Method

Since the previous paper was written (Banks-Sills, 1991, “Application of the Finite Element Method to Linear Elastic Fracture Mechanics,” Appl. Mech. Rev., 44, pp. 447–461), much progress has been made in applying the finite element method to linear elastic fracture mechanics. In this paper, the problem of calculating stress intensity factors in two- and three-dimensional mixed mode problems will be considered for isotropic and anisotropic materials. The square-root singular stresses in the neighborhood of the crack tip will be modeled by quarter-point, square and collapsed, triangular elements for two-dimensional problems, respectively, and by brick and collapsed, prismatic elements in three dimensions. The stress intensity factors are obtained by means of the interaction energy or M-integral. Displacement extrapolation is employed as a check on the results. In addition, the problem of interface cracks between homogeneous, isotropic, and anisotropic materials is presented. The purpose of this paper is to present an accurate and efficient method for calculating stress intensity factors for mixed mode deformation. The equations presented here should aid workers in this field to carry out similar analyses, as well as to check their calculations with respect to the examples described.

Sign in / Sign up

Export Citation Format

Share Document