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The effect of flow configuration on the distribution of internal stresses in rigid colloidal aggregates was investigated numerically for cluster-cluster aggregates with fractal dimensions ranging from 1.7 to 2.3. Stokesian dynamics was used to evaluate the hydrodynamic force on each monomer, while the internal inter-monomer interactions were calculated by applying force and torque balances on each primary particle. The examined two-dimensional flows were characterised by a mixing index L, that ranged from 0 (rotation) to 1 (elongation), with pure shear flow at L=0.5. Two regimes of motion were identified: for L0.7) they reach a steady orientation with respect to the flow field. A transition region, in which only part of the aggregates reaches the steady state, separates the two regimes. The steady state regime appeared more favourable to induce breakage or restructuring, because in this case the generated internal stresses are sustained in time, while in the rotational regime they vary cyclically. We showed that the greater effectiveness of elongation with respect to shear can be explained by relating the condition of breakage to the time-averaged value of the internal stress rather than to the instantaneous value. By exploiting this relationship, the information on the viscous stress required to break or restructure an aggregate in a particular flow configuration can be easily extended to a different flow type.