Modeling the mechanics of HMX detonation using a Taylor–Galerkin scheme

•An integrated algorithm for cyclotetramethylene tetranitramine (HMX) particle detonation that incorporates equations of state, Arrhenius kinetics, and mixing rules.•A stabilized Taylor–Galerkin finite element simulation algorithm with pressure and temperature equilibrium enforced across phases.•The scheme captures the distinct features of detonation waves: rarefaction wave, contact discontinuity, shock wave, and the von Neumann spike.•Computed detonation velocity compares well with experiments reported in literature.

Design of energetic materials is an exciting area in mechanics and materials science. Energetic composite materials are used as propellants, explosives, and fuel cell components. Energy release in these materials are accompanied by extreme events: shock waves travel at typical speeds of several thousand meters per second and the peak pressures can reach hundreds of gigapascals. In this paper, we develop a reactive dynamics code for modeling detonation wave features in one such material. The key contribution in this paper is an integrated algorithm to incorporate equations of state, Arrhenius kinetics, and mixing rules for particle detonation in a Taylor–Galerkin finite element simulation. We show that the scheme captures the distinct features of detonation waves, and the detonation velocity compares well with experiments reported in literature.