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A semi-infinite crack in infinite square lattice is subjected to a wavecoming from infinity, thereby leading to its scattering by the crack surfaces.A partially damaged zone ahead of the crack-tip is modeled by an arbitrarilydistributed stiffness of the damaged links. While the open crack, with anatomically sharp crack-tip, in the lattice has been solved in closed form withhelp of {the} scalar Wiener-Hopf formulation (SIAM Journal on AppliedMathematics, 75, 1171--1192; 1915--1940), the problem considered here becomesvery intricate depending on the nature of damaged links. For instance, in thecase of partially bridged finite zone it involves a $2\times2$ matrix kernel offormidable class. But using an original technique, the problem, including thegeneral case of arbitrarily damaged links, is reduced to a scalar one with theexception that it involves solving an auxiliary linear system of $N \times N$equations where $N$ defines the length of the damage zone. The proposed methoddoes allow, effectively, the construction of an exact solution. Numericalexamples and the asymptotic approximation of the scattered field far away fromthe crack-tip are also presented.

Scattering on square lattice from crack with damage zone