In this work, we characterize the nucleation and elongation mechanisms of the "diseased" polymorph of the amyloid-beta 40 (A beta 40) fibril using an off-lattice coarse-grained (CG) protein model. After determining the nucleation size and subsequent stable protofibrillar structure from the CG model, validated with all-atom simulations, we consider the "lock and dock" and "activated monomer" fibril elongation mechanisms for the protofibril by statistical additions of a monomer drawn from four different ensembles of the free A beta 40 peptide to grow the fibril. Our CG model shows that the dominant mechanism for fibril elongation is the lock and dock mechanism across all monomer ensembles, even when the monomer is in the activated form. Although our CG model finds no thermodynamic difference between the two fibril elongation mechanisms, the activated monomer is found to be kinetically faster by a factor of 2 for the "locking" step compared with all other structured or unstructured monomer ensembles.