Abstract
The driving force of fracture phenomena is the released energy by crack extension, which is expressed with J-integral in two-dimensional special case. In this paper, a generalization Jω (u, X) of J-integral is proposed, which has two parameters ω and X, in 2-D and 3-D general cases. Here u stands for the displacement vector. The symbol X express the vector field derived from the crack extension, and ω the domain where we get the information. The generalized J-integral Jω (u, X) is the sum of the integral Pω (u, X) over the line/surface ∂ω and the integral Rω (u, X) over the domain ω. The formula Jω (u, X) is derived in 1981 from the mathematical research of 3-D quasi-static fracture problems by the author. The integral Rω (u, X) is well defined for the weak solution of the variational problems from elasticity, by which we can express the energy release rate and applicable for finite element method.
