Particle Mechanics Approach to Modeling Impact Response and Wave Propagation in Bonded Particulate Systems
Particle mechanics approaches to modeling granular solids employ contact laws to determine interparticle forces and moments and time integrators to integrate the Euler-Lagrange equations of motion to obtain the dynamic behavior of the granular system. The aim of this thesis is to present these modeling approaches to study impact response and wave propagation in large bonded particular systems over long times. To achieve this aim, we develop a six-degree-of freedom momentum-preserving explicit time integrator that exhibits nearconservation of total energy and excellent stability over exponentially long times. We use a rescaled Rodriguez parameterization of particle attitude. In addition, we build a complex particle-binder-particle contact law between the particles to account for normal, tangential, torsional, and bending interactions transmitted through an elastic binder. This contact law also includes binder failure mechanisms in both tension and compression, and the resulting direct particle-particle interactions following binder failure. With this integrator and contact law, we explore the microstructural response of a plastic-bonded explosive composed of HMX crystals embedded in a Sylgard® binder to impacts at various velocities ranging from 10 m/s to 400 m/s. Our system includes nearly 100 000 particles and roughly 1.6 million contacts, allowing us to create probability distributions of stresses, strains, and velocities occuring throughout the simulation with a high statistical significance. The majority of the microstructural response appears to depend upon the axial strain more than upon the impact velocity, excepting the interparticle relative approach velocity. Because hotspot formation in PBXs under impact loading is known to occur above a threshold impact velocity, but not below, any physical phenomena related to the formation of such hotspots must also be dependent upon the impact velocity. Thus, we postulate that any rare events, such as the formation of hotspots that generate chain reactions in granular energetic assemblies, are tied to the interparticle approach velocities.