Crack propagation in finite elastodynamics

Within the framework of finite elastodynamics, a crack propagation analysis, for sheets of compressible hyperelastic material, is formulated. By exploiting a dynamic generalization of the Stephenson's result, 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 the asymptotic Piola-Kirchhoff and Cauchy stresses, on the determination of crack profile and of the vector energy flux at the moving crack tip. Moreover, the most important differences with respect to the classical predictions of linear elastodynamic theory are evidenced.