CHILES 2: a finite element computer program that calculates the intensities of linear elastic singularities in isotropic and orthotropic materials (original) (raw)
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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 purp...
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Application of singular quadratic distorted isoparametric elements in linear fracture mechanics
International Journal for Numerical Methods in Engineering, 1993
The understanding of the performance of the quarter-point and transition elements is of considerable importance as these singular elements are widely used in linear elastic fracture mechanics (LEFM) analyses. However, a number of issues remain unresolved although numerous investigations into their performance have been conducted. In particular is the question of optimum quarter-point element and transition-element size. This study examines several aspects in relation to the size effect by performing a large number of numerical analyses on several standard problems. Interpretation of the numerical results was aided by the use of two concepts, the 'zones of dominance' and 'zones of representation'. This study proposes a means of explaining the errors in stress intensity factor computation through the interaction between both types of zones. Consequently, a number of new and significant observations were made regarding the singular elements' performance. This study concludes with some recommendations for the application of these elements.
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This paper discusses the reproduction of the square root singularity in quarter-point tetrahedral (QPT) finite elements. Numerical results confirm that the stress singularity is modeled accurately in a fully unstructured mesh by using QPTs. A displacement correlation (DC) scheme is proposed in combination with QPTs to compute stress intensity factors (SIF) from arbitrary meshes, yielding an average error of 2 − 3%. This straightforward method is computationally cheap and easy to implement. The results of an extensive parametric study also suggest the existence of an optimum mesh-dependent distance from the crack front at which the DC method computes the most accurate SIFs.
Global journal of research in engineering, 2022
In linear elastic fracture mechanics, the stress field is singular at the tip of a crack. Since the representation of this singularity in a numerical model raises considerable numerical difficulties, the paper uses a strategy that regularizes the elastic field, subtracting the singularity from the stress field, known as the singularity subtraction technique (SST). In this paper, the SST is implemented in a local mesh-free numerical model, coupled with modern optimization schemes, used for solving twodimensional problems of the linear elastic fracture mechanics. The mesh-free numerical model (ILMF) considers the approximation of the elastic field with moving least squares (MLS) and implements a reduced numerical integration. Since the ILMF model implements the singularity subtraction technique that performs a regularization of the stress field, the mesh-free analysis does not require a refined discretization to obtain accurate results and therefore, is a very efficient numerical analysis.