THE EXPLICIT RELATION BETWEEN THE M-INTEGRAL AND THE ELASTIC MODULI OF INCLUSION/DAMAGES

The M-integral represents the energy release rate due to the self-similar expansion of defects in material configurational mechanics while the reduction of effective elastic moduli is an inner damage parameter in traditional damage mechanics. This study will focus on the inherent relation between them in order to build the bridge of material configurational mechanics and damage mechanics. The explicit expression of M-integral is derived by using Muskhelishvili complex potential for the infinite plane with a circle inclusion. And the explicit expression of M-integral reveals the explicit relation between M-integral and the elastic moduli of the inclusion. A finite element method analysis is then performed to simulate the complex defects embedded in an elastic-plastic plane. The results reveal the inherent relation between the reduction of the effective elastic moduli for damaged area and the M-integral. In conclusion, the M-integral as an outer variable is believed to be capable of replacing the inner variable (reduction of the effective moduli) to describe the defects evolution in damaged material.