ABSTRACT
The spatial average value of some physical variables in the form of weighted integration is defined by Bazant (1988) and it is stated that the physical variables related to non-linear strain softening behavior in constitutive relation, such as incremental plastic strain εpij , plastic multiplier λ or others should take their average values. The elastic variables which do not participate in the localization are still used in the local continuous models. The stress singularity at the crack of I-, II-, III-mode were discussed by Eringen (1977) using non-local theory within a wide range of frequency and wavelength. The effect of the lattice parameter of anisotropic materials on the stress field of crack tip under a uniform anti-plane shear loading is investigated by Sun et al. (2004) by means of non-local theory, and dependence of stress field at crack tip on crack length and crystal lattice dimension by means of Fourier transformation are discussed. The stress and strain fields near the crack tip of I mode crack are analyzed by Peerlings (2001) with use of non-local theory based on Gaussian weighted function and the results are compared with those obtained by strain-gradient model. Distributions of a certain physical variables are determined by weighted functions introduced in nonlocal fracture theory. Therefore, the choice of weighted function is a key to constitute to non-local strain softening model. In this paper, the relationship of different weighted functions and intrinsic length scale and their influence on non-local theory are discussed. Different distributions of stress field near the crack of the I-II mixed mode crack are compared by means of non-local model with different types of weighted functions.
