Context. There is an active debate about whether the properties of comets as observed today are primordial or, alternatively, if they are a result of collisional evolution or other processes. Aims. We investigate the effects of collisions on a comet with a structure like 67P/Churyumov-Gerasimenko (67P). We develop scaling laws for the critical specific impact energies Q reshape required for a significant shape alteration. These are then used in simulations of the combined dynamical and collisional evolution of comets in order to study the survival probability of a primordially formed object with a shape like 67P. Although the focus of this work is on a structure of this kind, the analysis is also performed for more generic bi-lobe shapes, for which we define the critical specific energy Q bil . The simulation outcomes are also analyzed in terms of impact heating and the evolution of the porosity. Methods. The effects of impacts on comet 67P are studied using a state-of-the-art smooth particle hydrodynamics shock physics code. In the 3D simulations, a publicly available shape model of 67P is applied and a range of impact conditions and material properties are investigated. The resulting critical specific impact energy Q reshape (as well as Q bil for generic bi-lobe shapes) defines a minimal projectile size which is used to compute the number of shape-changing collisions in a set of dynamical simulations. These simulations follow the dispersion of the trans-Neptunian disk during the giant planet instability, the formation of a scattered disk, and produce 87 objects that penetrate into the inner solar system with orbits consistent with the observed JFC population. The collisional evolution before the giant planet instability is not considered here. Hence, our study is conservative in its estimation of the number of collisions. Results. We find that in any scenario considered here, comet 67P would have experienced a significant number of shape-changing collisions, if it formed primordially. This is also the case for generic bi-lobe shapes. Our study also shows that impact heating is very localized and that collisionally processed bodies can still have a high porosity. Conclusions. Our study indicates that the observed bi-lobe structure of comet 67P may not be primordial, but might have originated in a rather recent event, possibly within the last 1 Gy. This may be the case for any kilometer-sized two-component cometary nuclei.

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