Energy release rate and J integral for cracks propagating in nonhomogeneous media Part I - Problem formulation - Suo, Xiao-Zheng; Combescure, Alain (European Journal of Computational Mechanics, 1993)
In this paper the energy release rate (or the j integral) is calculated for cracks propagating in media with spatially varying material characteristics. Without any assumption on the direction of such a variation with respect to the crack axis at it was made in a similar approach [ ATK 75], an analytical expression for the energy release rate under genera/loading conditions is derived and put in a form suitable for numerical analysis of an arbitrary 3D crack configuration. For cracks in nonhomogeneous media, it is shown that the equivalent J integral should contain, in the 2D deformation field, an additional surface integral (volume integral in the 3D case) to keep its we/known independence property when computed with different integration paths.