Driving force acting on a running crack

Abstract

The asymptotic analysis of the dynamic crack problem for the anti-plane shear mode is provided. The field near the crack tip is studied in detail for a nonlinear elastic incompressible material whose stored energy behaves asymptotically as a power of the first invariant of the strain tensor at large strains. It is shown that the hardening parameter characterizes fully the singularity degree of the near-crack-tip field. Based on the latter knowledge the driving force acting on the crack tip is calculated. Possible scenarios of the crack propagation are discussed.