On predicting the effective elastic properties of polymer bonded explosives using the recursive cell method

Polymer bonded explosives are particulate composites containing elastic particles in a viscoelastic binder. The particles occupy an extremely high fraction of the volume, often greater than 90%. Under low strain rate loading (∼0.001–1 s −1) and at room temperature and higher, the elastic modulus of the particles can be four orders of magnitude higher than that of the binder. Rigorous bounds and analytical estimates for the effective elastic properties of these materials have been found to be inaccurate. The computational expense of detailed numerical simulations for the determination of effective properties of these composites has led to the search for a faster technique. In this work, one such technique based on a real-space renormalization group approach is explored as an alternative to direct numerical simulations in determining the effective elastic properties of PBX 9501. The method is named the recursive cell method (RCM). The differential effective medium approximation, the finite element method, and the generalized method of cells (GMC) are investigated with regard to their suitability as homogenizers in the RCM. Results show that the RCM overestimates the effective properties of particulate composites and PBX 9501 unless large blocks of subcells are renormalized and the particles in a representative volume element are randomly distributed. The GMC homogenizer is found to provide better estimates of effective elastic properties than the finite element based homogenizer for composites with particle volume fractions less than 0.80.