Path-independent integral for heterogeneous media with respect to field discontinuities

By means of counter-evidence, it is proved that the original J integral does not satisfy the conservation law for general heterogeneous media. In the present paper, a modified version J∗ is re-proposed, which is a path-independent integral. The modifier term is related to stress and strain discontinuities occurring in material interfaces, and possibly occurring in interfaces between elastic and plastic zones. The integral J∗ can be interpreted as an expression of energy release rate, therefore, there exists an integral fracture criterion correspondingly. With regard to computational aspects related to finite element analysis, interface elements have been proposed to deal with stress and strain discontinuities in the material interfaces. For a generic case, adaptive analysis is recommended to take into account the discontinuities in the material interfaces, and possible discontinuities in the interfaces between elastic and plastic zones around a crack tip, in an optimal manner.