Finite element modeling of porous solid propellants

The effect of porosity on the constitutive response of a linearly viscoelastic solid that obeys a constitutive law of the standard differential form is investigated under small strain deformation conditions. It is demonstrated that a constitutive potential for the description of the porous material can be devised for any arbitrary combination of hydrostatic and deviatoric loadings. The potential is used to determine the associated 3-D stress-strain relationship in the form of hereditary viscoelastic integrals. The presence of porosity establishes relaxation time scales for the porous body that differ from the relaxation time of the pure matrix material and brings about a viscous character to the overall hydrostatic response. The constitutive law is implemented in the finite element code Rocsolid at our Center for Simulation of Advanced Rockets (CSAR) to study the response of solid propellant materials in which damage due to particle dewetting is modeled by the presence of porosity. Simulation results for the mechanical response of the Titan IV SRMU PQM-1 rocket motor indicate severe damage accumulation at the stress relief grooves and the grain/case interface where cracking was observed to initiate during a static test firing.