On the physical interpretation of the M-integral in nonlinear elastic defect mechanics

Several properties of the M-integral are clarified within the context of nonlinear elastic defect mechanics. A material damage expansion force vector associated with the integrand of the M-integral is derived by divergence vector operation of the Lagrangian energy density moment. It is concluded that the components of damage expansion force vector are indentified as the change of potential energy due to the self-similar expansion of one infinitesimal material element along the x₁ or x₂ direction. Subsequently, the physical interpretation of the M-integral over the contour enclosing all defects is explored in nonlinear elasticity containing multiple defects by an explicit analysis. The explicit analysis reveals that the M-integral is inherently related to the change of the total potential energy during the formation of defects from the initial non-damaged system in addition to the nonlinear strain energy within the area enclosed by integration contour.