ANTIPLANE PROBLEM OF A CRACK IN A LATTICE.

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Abstract

Dynamic and quasistatic propagation of rupture of bonds in a discrete model of an elastic medium is considered. It is demonstrated that there is an outflow of energy from the extremity of the ″cracks″ and it is determined how this energy depends on the crack velocity. Thus, a propagation criterion is derived for the crack on the macrolevel (critical stress intensity or critical energy flux) in terms of a characteristic of the microstructure. It is also shows that it is possible for a crack to propagate in a lattice at a velocity exceeding the shear wave velocity, i. e. , the limiting velocity for a crack in a continuous medium. To solve the problem, the continuous and disrete Fourier transforms and the Wiener-Hopf method are used. In relation to a discrete system, analogs of familiar formulas that are used in factorization, in particular a periodic analog of the Cauchy-type integral, are given, and a rule for selecting stationary solutions is validated.

Original languageEnglish
Pages (from-to)101-114
Number of pages14
JournalMechanics of Solids
Volume17
Issue number5
StatePublished - 1982

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