Energy release rate along any crack front in the thickness direction of shell elements

This paper deals with a numerical method for calculating the pro®le of the energy release rate G (or J-integral) along any crack front in the thickness direction of shell elements. For this purpose, the virtual crack extension technique is ®rstly used for its average evaluation throughout the entire shell thickness. Secondly, local values for points on the crack front are derived by assuming that the G parameter at any level in the shellʹs thickness direction is linearly proportional to the strain energy density of points at the same level in the region where HRR singular ®elds are dominant. Example computations show that the G parameter pro®le by the present method is in good agreement with that by alternative methods throughout a large range of elastic±plastic deformation