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We present a novel approach for the numerical solution of problems of elasticscattering by open arcs in two dimensions. Our methodology relies on thecomposition of weighted versions of the classical operators associated withDirichlet and Neumann boundary conditions in conjunction with a certain"open-arc elastic Calder\'on relation" whose validity is demonstrated in thispaper on the basis of numerical experiments, but whose rigorous mathematicalproof is left for future work. Using this Calder\'on relation in conjunctionwith spectrally accurate quadrature rules and the Krylov-subspace linearalgebra solver GMRES, the proposed overall open-arc elastic solver producesresults of high accuracy in small number of iterations---for low and highfrequencies alike. A variety of numerical examples in this paper demonstratethe accuracy and efficiency of the proposed methodology.

Weighted integral solvers for elastic scattering by open arcs in two dimensions