M–Integral and Energy-Release Rates: A Didactical Account

Within the framework of linear elasticity, the M-integral is connected to energy changes due to a self-similar expansion of a configuration. In this contribution, we will calculate the M-integral by evaluating a path-independent contour integral and by calculating the virial of material tractions active at boundaries and interfaces for the simple case of a hollow circular cylinder having an inclusion with and without misfit, loaded by external forces under plane stress/plane strain conditions. The connection between the similarity transformation of the total elastic potential and the M-integral is explored.