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Finite separation method: an efficient boundary element crack modeling technique

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Abstract

In computational fracture mechanics, great benefits are obtained from the reduced modeling dimension order and the accurate integral formulation of the boundary element method (BEM). However, the direct representation of co-planar surfaces (i.e., cracks) causes a degeneration of the standard displacement BEM formulation which can only be circumvented with special modeling techniques. Aiming to simplify the generalized application of the BEM to fracture mechanics problems, this paper presents a two-dimensional crack modeling approach. The method uses the direct BEM displacement formulation within a single-domain model to efficiently and precisely calculate any mixed mode crack tip stress intensity factor. Details of the application of the method are presented, while its accuracy and reliability are demonstrated through numerous comparisons with benchmark results.

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Abbreviations

a :

Crack length

e :

Relative error of integration

da :

Crack advance increment

G :

Shear modulus

h, h s, h t :

Element length

J :

Jacobian

K I, K II :

Mode I and II stress intensity factor

m :

Number of integration points

N :

Boundary element shape function

n i :

Vector component of the unit outward normal to Γ

p :

Singularity order

P :

Collocation point

Q :

Field point

r :

Distance between collocation point (P) and field point (Q) or distance from the crack tip

t i :

Traction component in direction i

T ij :

Traction kernel tensor component ij

u i :

Displacement component in direction i

U ij :

Displacement kernel tensor component ij

α :

Relative position of the midside node of a singular sub-element

β I, β II :

Mode I and II shape factor

γ :

Relative position of the midside node of a singular element

Γ:

Boundary of the analysed domain

δ :

Crack face separation

θ :

Angular position from the crack tip

ξ :

Element intrinsic local coordinate

υ :

Poisson’s ratio

ψ :

Crack face mesh refinement ratio (h s /h t )

Ω:

Analysed domain

BEM:

Boundary element method

DDM:

Displacement discontinuity method

DBEM:

Dual boundary element method

FEM:

Finite element method

FSM:

Finite separation method

QPE:

Quarter-point element

SIF:

Stress intensity factor

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Authors and Affiliations

  1. Civil Engineering Department, Université de Sherbrooke, Sherbrooke, QC, J1K 2R1, Canada

    Sébastien Lalonde

  2. Mechanical Engineering Department, École de Technologie Supérieure, Montréal, QC, H3C 1K3, Canada

    Raynald Guilbault

Authors
  1. Sébastien Lalonde
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  2. Raynald Guilbault
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Correspondence to Raynald Guilbault.

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Lalonde, S., Guilbault, R. Finite separation method: an efficient boundary element crack modeling technique. Comput Mech 44, 791–807 (2009). https://doi.org/10.1007/s00466-009-0408-1

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