  In this paper, we extend our Smooth Particle Hydrodynamics (SPH) impact code
to include the effect of porosity at a sub-resolution scale by adapting the
so-called $P-alpha$ model. Many small bodies in the different populations of
asteroids and comets are believed to contain a high degree of porosity and the
determination of both their collisional evolution and the outcome of their
disruption requires that the effect of porosity is taken into account in the
computation of those processes. Here, we present our model and show how
porosity interfaces with the elastic-perfectly plastic material description and
the brittle fracture model generally used to simulate the fragmentation of
non-porous rocky bodies. We investigate various compaction models and discuss
their suitability to simulate the compaction of (highly) porous material. Then,
we perform simple test cases where we compare results of the simulations to the
theoretical solutions. We also present a Deep Impact-like simulation to show
the effect of porosity on the outcome of an impact. Detailed validation tests
will be presented in a next paper by comparison with high-velocity laboratory
experiments on porous materials (Jutzi et al., in preparation). Once validated
at small scales, our new impact code can then be used at larger scales to study
impacts and collisions involving brittle solids including porosity, such as the
parent bodies of C-type asteroid families or cometary materials, both in the
strength- and in the gravity-dominated regime.
