An interpretation of the internal length in Chang's couple-stress continuum for bonded granulates

Theoretical investigation into bonded granulates is of great importance to modern geomechanics. This paper presents an interpretation of the internal length in Chang's couple-stress continuum for bonded materials (Chang et al., Eng Fract Mech 69(17):1941-1958, 2002; Chang and Shi, J Eng Mech ASCE 131(2):120-130, 2005). First, a micro-model for bonds between particles is proposed, in which a pair of bonded particles is in contact over a width B and this bond contact width is continuously distributed with the normal/tangential basic elements (BE) (each BE is composed of spring, dashpot, bond, slider or divider). Second, a couple model for the bonds is established to describe the relationship between relative particle rotation and couple. Third, Chang's couple-stress continuum for bonded material is analyzed in the case of a hexagonal packing structure of a monodisperse bonded material. The study shows that the internal length in Chang's couple-stress continuum for bonded monodisperse material is equal to root 3B/6, while other usual elastic constants of the continuum can also be linked to B. In addition, those constants can be associated with a size-independent parameter proposed in this paper.