### Abstract

It is well known that boundary integral formulations degenerate for a body containing flat cracks. The methods used to analyse fracture problems include multi-region approaches and Green's function formulations. Recently a displacement discontinuity method has also been used to solve fracture problems. In this method the displacement discontinuity along the crack surface is related to the applied traction through an integral equation. The technique adapted for solving this equation requires that the gradient of the displacement discontinuity be continuous across the element boundaries. This can be ensured only if the gradients of the displacement discontinuity is also interpolated in addition to the displacement discontinuities. For two dimensional problems this would result in doubling the number of nodal variables. In the proposed method the integral equation relating the displacement discontinuities to the applied traction is solved directly by using the Hadamard's principle. This method requires only that the points at which the stresses are evaluated be distinct from the element nodes. This technique is found to yield satisfactory results for various problems including multi-cracks, non-uniform loading and both infinite space and half space problems.

Original language | English |
---|---|

Pages (from-to) | 141-145 |

Number of pages | 5 |

Journal | Engineering Fracture Mechanics |

Volume | 39 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 1991 |

### Fingerprint

### ASJC Scopus subject areas

- Mechanical Engineering
- Mechanics of Materials

### Cite this

**Hadamard's principle for displacement discontinuity modeling of cracks.** / Chaoxi, Ling; Suaris, Wimal.

Research output: Contribution to journal › Article

*Engineering Fracture Mechanics*, vol. 39, no. 1, pp. 141-145. https://doi.org/10.1016/0013-7944(91)90029-Z

}

TY - JOUR

T1 - Hadamard's principle for displacement discontinuity modeling of cracks

AU - Chaoxi, Ling

AU - Suaris, Wimal

PY - 1991/1/1

Y1 - 1991/1/1

N2 - It is well known that boundary integral formulations degenerate for a body containing flat cracks. The methods used to analyse fracture problems include multi-region approaches and Green's function formulations. Recently a displacement discontinuity method has also been used to solve fracture problems. In this method the displacement discontinuity along the crack surface is related to the applied traction through an integral equation. The technique adapted for solving this equation requires that the gradient of the displacement discontinuity be continuous across the element boundaries. This can be ensured only if the gradients of the displacement discontinuity is also interpolated in addition to the displacement discontinuities. For two dimensional problems this would result in doubling the number of nodal variables. In the proposed method the integral equation relating the displacement discontinuities to the applied traction is solved directly by using the Hadamard's principle. This method requires only that the points at which the stresses are evaluated be distinct from the element nodes. This technique is found to yield satisfactory results for various problems including multi-cracks, non-uniform loading and both infinite space and half space problems.

AB - It is well known that boundary integral formulations degenerate for a body containing flat cracks. The methods used to analyse fracture problems include multi-region approaches and Green's function formulations. Recently a displacement discontinuity method has also been used to solve fracture problems. In this method the displacement discontinuity along the crack surface is related to the applied traction through an integral equation. The technique adapted for solving this equation requires that the gradient of the displacement discontinuity be continuous across the element boundaries. This can be ensured only if the gradients of the displacement discontinuity is also interpolated in addition to the displacement discontinuities. For two dimensional problems this would result in doubling the number of nodal variables. In the proposed method the integral equation relating the displacement discontinuities to the applied traction is solved directly by using the Hadamard's principle. This method requires only that the points at which the stresses are evaluated be distinct from the element nodes. This technique is found to yield satisfactory results for various problems including multi-cracks, non-uniform loading and both infinite space and half space problems.

UR - http://www.scopus.com/inward/record.url?scp=0025750590&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0025750590&partnerID=8YFLogxK

U2 - 10.1016/0013-7944(91)90029-Z

DO - 10.1016/0013-7944(91)90029-Z

M3 - Article

VL - 39

SP - 141

EP - 145

JO - Engineering Fracture Mechanics

JF - Engineering Fracture Mechanics

SN - 0013-7944

IS - 1

ER -