L. Gorbatikh et M. Kachanov, A simple technique for constructing the full stress and displacement fields in elastic plates with multiple cracks, ENG FRACT M, 66(1), 2000, pp. 51-63
Full displacement and stress fields in a two-dimensional elastic solid with
multiple interacting cracks is constructed in an approximate way, in eleme
ntary functions. It is done by approximating the actual displacement discon
tinuity (COD) on each crack, in each of modes I and II, by a product of the
ellipse corresponding to an isolated crack and a quadratic polynomial. The
polynomial's coefficients, that reflect crack interactions, are chosen to
match the SIFs and the average tractions on cracks (quantities found, for e
xample, by a simple method of analysis of crack interactions; Kachanov, M.
Elastic solids with many cracks: a simple method of analysis. International
Journal of Solids and Structures, 23, 1987. 23-43). We then use this appro
ximated CODs in the representation of the displacement field in the solid i
n terms of integrals over crack lines, with CODs as kernels. The constructe
d field differs from the actual one by the field generated by such traction
distributions on cracks that have zero averages and produce zero stress in
tensity factors. The accuracy of the suggested method depends on the config
uration, but, generally, remains good at spacings between cracks that are s
ubstantially smaller than the crack lengths. (C) 2000 Elsevier Science Ltd.
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