  The microscopic description of heavy-ion reactions at low beam energies is
achieved within hadronic transport approaches. In this article a new approach
SMASH (Simulating Many Accelerated Strongly-interacting Hadrons) is introduced
and applied to study the production of non-strange particles in heavy-ion
reactions at $E_{\rm kin}=0.4-2A$ GeV. First, the model is described including
details about the collision criterion, the initial conditions and the resonance
formation and decays. To validate the approach, equilibrium properties such as
detailed balance are presented and the results are compared to experimental
data for elementary cross sections. Finally results for pion and proton
production in C+C and Au+Au collisions is confronted with HADES and FOPI data.
Predictions for particle production in $\pi+A$ collisions are made.
