We present an implementation of stellar evolution and chemical feedback for smoothed particle hydrodynamics simulations. We consider the timed release of individual elements by both massive (Type II supernovae and stellar winds) and intermediate-mass stars (Type Ia supernovae and asymptotic giant branch stars). We illustrate the results of our method using a suite of cosmological simulations that include new prescriptions for radiative cooling, star formation and galactic winds. Radiative cooling is implemented element-by-element, in the presence of an ionizing radiation background, and we track all 11 elements that contribute significantly to the radiative cooling. While all simulations presented here use a single set of physical parameters, we take specific care to investigate the robustness of the predictions of chemodynamical simulations with respect to the ingredients, the methods and the numerical convergence. A comparison of nucleosynthetic yields taken from the literature indicates that relative abundance ratios may only be reliable at the factor of 2 level, even for a fixed initial mass function. Abundances relative to iron are even more uncertain because the rate of Type Ia supernovae is not well known. We contrast two reasonable definitions of the metallicity of a resolution element and find that while they agree for high metallicities, there are large differences at low metallicities. We argue that the discrepancy is indicative of the lack of metal mixing caused by the fact that metals are stuck to particles. We argue that since this is a (numerical) sampling problem, solving it by using a poorly constrained physical process such as diffusion could have undesired consequences. We demonstrate that the two metallicity definitions result in redshift z = 0 stellar masses that can differ by up to a factor of 2, because of the sensitivity of the cooling rates to the elemental abundances. Finally, we use several 5123 particle simulations to investigate the evolution of the distribution of heavy elements, which we find to be in reasonably good agreement with available observational constraints. We find that by z = 0 most of the metals are locked up in stars. The gaseous metals are distributed over a very wide range of gas densities and temperatures. The shock-heated warm-hot intergalactic medium has a relatively high metallicity of ~10-1Zsolar that evolves only weakly, and is therefore an important reservoir of metals. Any census aiming to account for most of the metal mass will have to take a wide variety of objects and structures into account.