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On the finite motions generated by a mode I propagating crack. (English) Zbl 1005.74055

Summary: We investigate the motion field surrounding a rapidly propagating crack loaded symmetrically about the crack plane. The problem is formulated within the framework of finite elastodynamics for thin slabs composed of compressible hyperelastic material. Writing the equations of motion together with initial and internal boundary conditions (in a coordinate system that translates with the moving crack tip), we perform an asymptotic local analysis of a traction-free straight crack that suddenly grows at constant velocity. Moreover, asymptotic Piola-Kirchhoff and Cauchy stress fields are computed, and we discuss the order of singularity of dynamic stresses.

MSC:

74R10 Brittle fracture
74H35 Singularities, blow-up, stress concentrations for dynamical problems in solid mechanics
74B20 Nonlinear elasticity
74H10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of dynamical problems in solid mechanics
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