The interaction between multiple shells in a MWNT structure is still a subject of intense research for theoreticians as well as experimentalists1-4. Uncertainties arise mainly from the difficulties in calculating the atomic interactions within the material, i.e. graphite sliding5. In contrast, the other relevant deformation mode; separation, can be modeled through a modified Lennard Jones potential6. Accepting the validity of continuum mechanics at the relevant scales7 it is possible to define a parameter that while varying from zero to one, spans from frictionless sliding to perfect bonding between individual layers8. Each individual graphene sheet making a nanotube is considered an isotropic hollow cylinder with a thickness equal to that of the equilibrium separation between layers, leaving no space between layers, in agreement with arguments presented elsewhere9. The key point of this analysis is the modeling of those interfaces through a single parameter called the shear transfer efficiency. Three loading situations are of interest: extension, twisting and bending. All three have in common that the load is introduced only to the outermost layer and somehow must be transferred to the inner shells. An implicit assumption is that the only stresses responsible for stress transfer between shells are shearing, although there is always normal stress transfer due to Poisson's effects and to the kinematics of the deformation, they are deemed to be of second order due to the low value of Poisson's ratio for graphene and are neglected in the present analysis. Their quantification would lead to the normal transfer efficiency, by analogy with our shear transfer efficiency.

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