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Crack in a 2D beam lattice: Analytical solutions for two bending modes by Michael Ryvkin; Leonid Slepyan is a Engineering article available to read on EtoBox.

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We consider an infinite square-cell lattice of elastic beams with a semi-infinite crack. Symmetric and antisymmetric bending modes of fracture under remote loads are examined. The related long-wave asymptotes corresponding to a continuous anisotropic bending plate are also considered. In the latter model, the symmetric mode is characterized by the square-root type singularity, whereas the antisymmetric mode results in a hyper-singular field. A solution for the continuous plate with a finite crack is also presented. These closed-form continuous solutions describe the fields in the whole plane. The main goal is to establish analytical connections between the 'macrolevel' state, defined by the continuous asymptote of the lattice solution, and the maximal bending moment in the crack-front beam, that is, to determine the resistance of the lattice with an initial crack to the crack advance. The solutions are obtained in the same way as for mass-spring lattices. Considering the static problems we use the discrete Fourier transform and the Wiener-Hopf technique. Monotonically distributed bending moments ahead of the crack are determined for the symmetric mode, and a selfequilibrated transv

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Author

Michael Ryvkin; Leonid Slepyan

Publisher

Elsevier Science; Elsevier ; Elsevier Ltd.; Elsevier BV (ISSN 0022-5096)

Published

2010

Language

EN

Field

Engineering (Physical Sciences)