Computational Physics Group

Karel Matous









Multiscale modeling of solid propellants: From particle packing to failure

K. Matous1,2, H.M Inglis1, X. Gu1, D. Rypl3, T.L Jackson1 and P.H. Geubelle1,2

1Center for Simulation of Advanced Rockets
2Department of Aerospace Engineering
University of Illinois at Urbana-Champaign
Urbana, IL 61801, USA.

3Department of Structural Mechanics
Czech Technical University in Prague
Prague, 160 00 P6, Czech Republic


We present a theoretical and computational framework for modeling the multiscale constitutive behavior of highly filled elastomers, such as solid propellants and other energetic materials. Special emphasis is placed on the effect of the particle debonding or dewetting process taking place at the microscale and on the macroscopic constitutive response. The microscale is characterized by a periodic unit cell, which contains a set of hard particles (such as ammonium perchlorate for AP-based propellants) dispersed in an elastomeric binder. The unit cell is created using a packing algorithm that treats the particles as spheres or discs, enabling us to generate packs which match the size distribution and volume fraction of actual propellants. A novel technique is introduced to characterize the pack geometry in a way suitable for meshing, allowing for the creation of high-quality periodic meshes with refinement zones in the regions of interest. The proposed numerical multiscale framework, based on the mathematical theory of homogenization, is capable of predicting the complex, heterogeneous stress and strain fields associated, at the microscale, with the nucleation and propagation of damage along the particle–matrix interface, as well as the macroscopic response and mechanical properties of the damaged continuum. Examples involving simple unit cells are presented to illustrate the multiscale algorithm and demonstrate the complexity of the underlying physical processes.


A fully automated mathematical/numerical framework for multiscale modeling of heterogeneous propellants from particle packing to failure has been presented. The microscale description is based on a periodic unit cell consisting of particles dispersed in a blend and incorporates the local non-homogeneous stress and deformation fields present in the unit cell during the failure of the particle/matrix interfaces. A packing algorithm, treating the embedded particles as spheres or discs, is used to generate packs which match the size distribution and volume fraction of actual propellants. Moreover, a sophisticated pre-processing tool has been developed to generate a geometric model based on Bezier curves and/or surfaces. This geometric model is then used in a general meshing tool, T3d, to create high-quality periodic meshes. Since the identical meshing of the periodic entities using the advancing front technique is not usually viable, a different approach based on mirroring has been adopted. Next, the mathematical theory of homogenization based on the asymptotic expansion of the displacement, strain and stress fields has been derived and used in modeling debonding (or dewetting) damage evolution in reinforced elastomers.

Various examples involving 2D unit cells and macroscopic deformation histories of an idealized solid propellant have been considered to study the link between the failure process taking place at the particle size scale and its effect on the macroscopic stress–strain curves and the evolution of void volume. The emphasis of this work has been to develop a damage analysis tool at multiple scales from particle packing to failure. Further research will involve the inclusion of large deformations, a more complex, rate-dependent description of the binder and a matrix tearing model needed to capture the initiation and propagation of cracks in the solid propellant during void coalescence. Moreover, the size of the representative volume element in the presence of damage needs to be investigated.


The work of K. Matous, H.M. Inglis, X. Gu, T.L. Jackson and P.H. Geubelle was supported by the Center for Simulation of Advanced Rockets (CSAR) under contract number B341494 by the U.S. Department of Energy as a part of its Advanced Simulation and Computing program (ASC). K. Matous and P.H. Geubelle also acknowledge support from ATK/Thiokol, with J. Thompson and Dr. I.L. Davis as a program monitors. The work of Dr. Rypl was supported by the Grant Agency of the Czech Republic under contract number GACR 103/05/2315.
© 2009 Notre Dame and Dr. Karel Matous