Journal of Xi'an Jiaotong Universtity

Comparative Analysis to NonLocal Theories Based on Different Types of Weighted Functions
Wang Zhongchang^1，2，Luan Maotian^1，2，Yang Qing^1，2
（1.State Key Laboratory of Coastal and Offshore Engineering，Dalian University of Technology，Dalian 116024，China；2．School of Civil and Hydraulic Engineering，Dalian University of Technology，Dalian 116024，China）

Abstract：To investigate the essential characteristics together with optimum selection of weighted functions in nonlocal theories，the influence area of the weighted functions and the dependency on internal length scale are examined for a number of commonlyused types of weighted functions，and the strain field in the neighborhood of the tip of Ⅰ-Ⅱ mixed mode crack is analyzed with the nonlocal theories based on different types of weighted functions．It is shown that the singularity of the strain field at the crack tip is smoothed in nonlocal theory．Compared with the strain from the classical fracture mechanics， the nonlocal strain is considerably reduced， and the larger the internal length scale，the more significant the reduction of nonlocal strain with respect to the local strain predicted conventionally．Furthermore，the effects of the stress intensity factors on all strain components at crack tip are investigated．
Keywords：nonlocal；weighted function； internal length scale；mixed mode crack；stress intensity factor；singularity