# A hybrid analytic–numerical method for three-dimensional cracks

S. H. Ju, H. H. Hsu

Research output: Contribution to journalArticle

1 Citation (Scopus)

### Abstract

This paper applied a hybrid analytic and numerical method to determine the displacement field and stress intensity factors of cracks in a three-dimensional (3D) body. First, an analytic solution including primary and shadow solutions of a semi-infinite crack in a 3D elastic body was developed, where the primary solutions are the traditional plane-strain solutions and the shadow ones are based on the 3D equilibrium equation. Only the multiplying factors of these solutions need to be determined, and they are constant in each plane perpendicular to the crack surface. A least-squares method incorporating the finite element results was used to determine these factors. If enough primary and shadow solutions are included, the proposed method can obtain an accurate displacement field for 3D crack problems. The major advantage of this method is that a 3D whole displacement field with the analytic singular effect near the crack tip can be obtained.

Original language English 262-275 14 Theoretical and Applied Fracture Mechanics 85 https://doi.org/10.1016/j.tafmec.2016.03.009 Published - 2016 Oct 1

### Fingerprint

Hybrid Method
Crack
cracks
Cracks
Three-dimensional
Surface Crack
Elastic body
Plane Strain
Crack Tip
Stress Intensity Factor
Least Square Method
Analytic Solution
Perpendicular
three dimensional bodies
elastic bodies
Numerical Methods
equilibrium equations
surface cracks
stress intensity factors
Finite Element

### All Science Journal Classification (ASJC) codes

• Materials Science(all)
• Condensed Matter Physics
• Mechanical Engineering
• Applied Mathematics

### Cite this

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title = "A hybrid analytic–numerical method for three-dimensional cracks",
abstract = "This paper applied a hybrid analytic and numerical method to determine the displacement field and stress intensity factors of cracks in a three-dimensional (3D) body. First, an analytic solution including primary and shadow solutions of a semi-infinite crack in a 3D elastic body was developed, where the primary solutions are the traditional plane-strain solutions and the shadow ones are based on the 3D equilibrium equation. Only the multiplying factors of these solutions need to be determined, and they are constant in each plane perpendicular to the crack surface. A least-squares method incorporating the finite element results was used to determine these factors. If enough primary and shadow solutions are included, the proposed method can obtain an accurate displacement field for 3D crack problems. The major advantage of this method is that a 3D whole displacement field with the analytic singular effect near the crack tip can be obtained.",
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In: Theoretical and Applied Fracture Mechanics, Vol. 85, 01.10.2016, p. 262-275.

Research output: Contribution to journalArticle

TY - JOUR

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AU - Ju, S. H.

AU - Hsu, H. H.

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AB - This paper applied a hybrid analytic and numerical method to determine the displacement field and stress intensity factors of cracks in a three-dimensional (3D) body. First, an analytic solution including primary and shadow solutions of a semi-infinite crack in a 3D elastic body was developed, where the primary solutions are the traditional plane-strain solutions and the shadow ones are based on the 3D equilibrium equation. Only the multiplying factors of these solutions need to be determined, and they are constant in each plane perpendicular to the crack surface. A least-squares method incorporating the finite element results was used to determine these factors. If enough primary and shadow solutions are included, the proposed method can obtain an accurate displacement field for 3D crack problems. The major advantage of this method is that a 3D whole displacement field with the analytic singular effect near the crack tip can be obtained.

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