Dual analysis for path integrals and bounds for crack parameter

dual analysis for the path integrals is carried out theoretically and numerically. As a dual form of Riceʹs J-integral, an alternative path-independent/*-integral is suggested in the paper, which can be formulated as the complementary energy release rate for the linear/nonlinear elasticity fracture system with a blunting crack model. As an energy functional of the stress and displacement, /* is equivalent to J in value since the effect of the stress distributions on the front of crack is included in its formulation. Dealing with bound estimation problems for crack parameters, the upper and lower bound theorems are described, respectively. /* is useful by the fact that its approximate solution is able to provide an upper bound for the exact one, and that it will enable the hybrid finite element to be a power role in fracture calculations. A series of numerical results is offered to verify the points mentioned in the paper. © 1998 Elsevier Science Ltd