On the finite motions generated by a mode I propagating crack

The motion field surrounding a rapidly propagating crack, loaded symmetrica lly about the plane of the crack, is investigated. The problem is formulate d within the framework of finite elastodynamics for thin slabs composed of compressible hyperelastic material. Writing the motion equations, the initi al and the internal boundary conditions, with respect to a coordinate syste m that translates with the moving crack tip, we perform an asymptotic local analysis for a traction-foe straight crack that suddenly grows at constant velocity. Moreover, the asymptotic Piola-Kirchhoff and Cauchy stress Field s are computed, and we discuss the order of singularity of the dynamic stre sses.