We present here a new theoretical model designed to explain the interstellar dust grain size distribution function (IDGSDF), and compare its results with previous observationally derived distributions and with previous theoretical models. The range of grain sizes produced in the late stages of stars with different masses is considered, and folded into a model which takes into account the observed changes in the historical local star formation rate. Stars in different mass ranges reach their grain producing epochs at times whose mass dependence is quantifiable, and the range of grain sizes produced has also been estimated as a function of stellar mass. The results show an IDGSDF that has a global slope comparable to the observationally derived plot and three peaks at values of the grain radius comparable to those in the observationally derived distribution, which have their ultimate origin in three major peaks which have been observed in the star formation rate (SFR) over the past 15 Gyr. The model uses grain-grain interactions to modify pre-existing size distributions at lower grain sizes, where collisions appear more important. The interactions include disruption by collisions as well as coagulation to form larger grains. The initial distributions are given a range of initial functions (flat, Gaussian, fractal) for their physical parameters, as well as geometrical forms ranging from spherical to highly elongated. The particles are constrained in an imaginary box, and laws of inelastic collisions are applied. Finally, we combine the two models and produce an IDGSDF which is a notably good match to the observational fit, and specifically at small grain radii reproduces the data better than the "SFR model" alone.