The Two-Dimensional Stress Problem Solved Using an Electric Digital Computer

Nisitani, Hironobu

doi:10.1299/jsme1958.11.14

Cited by 85 publications

(41 citation statements)

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“…The body force method (NISHITANI, 1968;NISHITANI et al, 1990) was used to determine the stress intensity factor and the inner pressure. The body force method allows us to examine the effect of confining pressure on the apparent fracture toughness, under the condition in which the extent of the cohesive zone is not negligibly small.…”

Section: Numerical Proceduresmentioning

confidence: 99%

Cohesive Crack Analysis of Toughness Increase Due to Confining Pressure

Sato

Hashida

2006

Pure appl. geophys.

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Apparent fracture toughness in Mode I of microcracking materials such as rocks under confining pressure is analyzed based on a cohesive crack model. In rocks, the apparent fracture toughness for crack propagation varies with the confining pressure. This study provides analytical solutions for the apparent fracture toughness using a cohesive crack model, which is a model for the fracture process zone. The problem analyzed in this study is a fluid-driven fracture of a two-dimensional crack with a cohesive zone under confining pressure. The size of the cohesive zone is assumed to be negligibly small in comparison to the crack length. The analyses are performed for two types of cohesive stress distribution, namely the constant cohesive stress (Dugdale model) and the linearly decreasing cohesive stress. Furthermore, the problem for a more general cohesive stress distribution is analyzed based on the fracture energy concept. The analytical solutions are confirmed by comparing them with the results of numerical computations performed using the body force method. The analytical solution suggests a substantial increase in the apparent fracture toughness due to increased confining pressures, even if the size of the fracture process zone is small.

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Section: Numerical Proceduresmentioning

confidence: 99%

Cohesive Crack Analysis of Toughness Increase Due to Confining Pressure

Sato

Hashida

2006

Pure appl. geophys.

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“…In this study, the body force method (33) is used to formulate the elastic stress concentration problem of Fig. 1 as a system of singular integral equations.…”

Section: The Proposed Modelmentioning

confidence: 99%

“…The first and second terms of Eq. (1) represent the stress due to the body force distributed on the imaginary boundary, which is composed of the internal or external points that are infinitesimally apart from the initial boundary (33) . Taking K Fr j nnM i (α j ,ψ i ) for example, the notation means the normal stress σ nM i induced at the point when a ring force F r j in the r-direction is acting on the imaginary boundary in bimaterial body "M 1 " or "M 2 ".…”

Section: Numerical Solutionsmentioning

confidence: 99%

Interaction among Ellipsoidal Inclusions and a Bimaterial Interface

Noda

Ono

Moriyama

2005

JSME Int. J., Ser. A

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Ellipsoidal inclusions can be regarded as a general model of defects in structures because they cover a lot of particular cases, such as line, circular and spherical defects. This paper deals with three-dimensional stress analysis for ellipsoidal inclusions in a bimaterial body under tension. The problem is formulated as a system of singular equations with Cauchy-type or logarithmic-type singularities, where unknowns are densities of body forces distributed in the r-and z-directions in bimaterial bodies having the same elastic constants of those of the given problem. In order to satisfy the boundary conditions along the ellipsoidal boundary, four types of fundamental density functions proposed in the previous paper are applied. Then the body force densities are approximated as a linear combination of fundamental density functions and polynomials. The present method is found to yield rapidly converging numerical results for stress distribution along the boundaries of both the matrix and inclusion even when the inclusion is very close to the bimaterial interface. Then, the effect of bimaterial surface on the stress concentration factor is discussed with varying the distance from bimaterial interface, shape ratio, and elastic modulus ratio.

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“…There are however several popular numerical methods, that can be used in the calculation of stress intensity factors in three-dimensional fracture mechanics. They include the ÿnite element method, see Zienkiewicz, 1 the body force method by Nisitani 2 and the boundary element method by Balas et al 3 Various techniques can be used to determine stress intensity factors at crack tips from an elastic analysis (see, for instance, Reference 4).…”

Section: Introductionmentioning

confidence: 99%

A variational technique for boundary element analysis of 3D fracture mechanics weight functions: static

Wen

Aliabadi

Rooke³

1998

Int. J. Numer. Meth. Engng.

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The dual boundary element method coupled with the weight function technique is developed for the analysis of three-dimensional elastostatic fracture mechanics mixed-mode problems. The weight functions used to calculate the stress intensity factors are deÿned by the derivatives of traction and displacement for a reference problem. A knowledge of the weight functions allows the stress intensity factors for any loading on the boundary to be calculated by means of a simple boundary integration without singularities. Values of mixedmode stress intensity factors are presented for an edge crack in a rectangular bar and a slant circular crack embedded in a cylindrical bar, for both uniform tensile and pure bending loads applied to the ends of the bars. ? 1998 John Wiley & Sons, Ltd.

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The Two-Dimensional Stress Problem Solved Using an Electric Digital Computer

Cited by 85 publications

References 0 publications

Cohesive Crack Analysis of Toughness Increase Due to Confining Pressure

Cohesive Crack Analysis of Toughness Increase Due to Confining Pressure

Interaction among Ellipsoidal Inclusions and a Bimaterial Interface

A variational technique for boundary element analysis of 3D fracture mechanics weight functions: static

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