Abstract: In this paper, we consider path-independent integrals and fracture criteria in nonlinear fracture dynamics. The dynamic effect and crack propagation are included in the discussion. Both nonlinear elastic and elastic-plastic case for crack propagation have been considered, and the related path-independent integrals are proposed. As an example, the steady state propagation of crack has been discussed. Lastly, we give the mechanical meaning of this path-independent integrals as the crack extension force, and make it possible to use the path-independent integrals (as fracture criterion in nonlinear fracture dynamics).

Key words: liquid sloshing, force, moment, liquid-solid coupled system