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Analytical solutions of dynamic mode I crack under the conditions of displacement boundary. (English) Zbl 1321.74061

Summary: Using complex analysis techniques, the problems of dynamic mode I crack under the condition of displacement boundary are investigated. For this kind of dynamic crack extension problems with arbitrary index of self-similarity, the universal representations of analytical solutions are facilely deduced by the methods of self-similar functions. Analytical solutions for the stresses, displacements and stress intensity factors are readily acquired using the methods of self-similar functions. The problems studied can be easily translated into Riemann-Hilbert problems, and their closed solutions are gained rather straightforward in terms of this technique. According to the corresponding material properties, the rule for the stress intensity factor was illustrated. Using those solutions and superposition theorem, the solutions of arbitrarily complex problems can be attained.

MSC:

74R10 Brittle fracture
74S70 Complex-variable methods applied to problems in solid mechanics
74H35 Singularities, blow-up, stress concentrations for dynamical problems in solid mechanics
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