Machine-precision fracture mechanics evaluations with the consistent boundary element method

Resumo

As hitherto proposed in the technical literature, the boundary element modelling of cracks is best carried

out resorting to a hypersingular fundamental solution. A more natural approach might rely on the direct representa-
tion of the crack tip singularity, as already proposed in the frame of the hybrid boundary element method. However,

recent mathematical assessments indicate that the conventional boundary element formulation – based on Kelvin’s

fundamental solution – is in fact able to precisely represent high stress gradients and deal with extremely convo-
luted topologies. We propose in this paper that independently of configuration a cracked structure be geometrically

represented as it would appear in real-world laboratory experiments, with crack openings in the range of microm-
eters or less. Owing to a newly developed integration scheme for two-dimensional problems, machine precision

evaluation of all quantities may be achieved and stress results consistently evaluated at interior points arbitrarily
close to crack tips. Importantly, no artificial topological issues are introduced and linear algebra conditioning is

kept under control. Some numerical illustrations show that highly accurate results are obtained for cracks rep-
resented with just a few quadratic, generally curved, boundary elements and a few Gauss-Legendre integration

points per element. The numerical evaluation of the J-integral turns out to be straightforward and actually the most
reliable means of obtaining stress intensity factors.