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Crack propagation in finite elastodynamics. (English) Zbl 1133.74036
Summary: Within the framework of finite elastodynamics, we perform a crack propagation analysis for sheets of compressible hyperelastic material. By exploiting a dynamic generalization of R. A. Stephenson’s result [J. Elasticity 12, 65–99 (1982; Zbl 0502.73079)], general far-field loading conditions are considered. Through an asymptotic singular analysis, the motion and the stress fields around a dynamically moving crack tip are then computed. Emphasis is placed on the order of singularity in asymptotic Piola-Kirchhoff and Cauchy stresses, on the determination of crack profile and of the vector energy flux at moving crack tip. Moreover, the most important differences with respect to the classical predictions of linear elastodynamic theory are evidenced.

MSC:
74R10 Brittle fracture
74B20 Nonlinear elasticity
74H40 Long-time behavior of solutions for dynamical problems in solid mechanics
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