Energetics of two circular inclusions in anti-plane elastostatics

In this paper, we use the recently derived solution of two circular elastic inclusions under anti-plane shear deformation (Honein et al., 1992a, b) to evaluate the material forces, as well as expanding and rotating moments `actingʹ on inclusions. These may be de®ned as the energy changes (e.g. energy release rates) accompanying unit translation, self-similar expansion and rotation of inclusions, respectively. The bond between the inclusions and the matrix is assumed to be perfect and the calculation is performed using the concept of the J, M and L path- independent integrals, respectively. The results obtained are valid under arbitrary loading. An illustrative example shows that two circular holes under remote uniform shear stress attract each other and that the J and M integrals grow without bound as the two holes become in®nitely close. A careful examination of the expression for these integrals yields the result that the J and M integrals tend to in®nity proportionally to 1=  e p , where e is a non-dimensional distance between the holes. It is also noticed that the J integral decays rapidly to zero as the two holes become four or ®ve radii apart. Other examples of two circular holes and inclusions under various stress ®elds are also considered and discussed