Semester of Graduation

Summer 2026

Degree

Master of Science in Mechanical Engineering (MSME)

Department

Mechanical Engineering

Document Type

Thesis

Abstract

Granular energetic materials (EMs) exhibit stochastic shock initiation because pore collapse, frictional dissipation, and localized thermal activation depend on microstructural descriptors that vary between nominally identical samples. Fully resolved mesoscale and atomistic calculations can represent these mechanisms, but their computational cost limits direct ensemble evaluation of microstructure-conditioned criticality thresholds. This thesis introduces a reduced-order framework for stochastic criticality estimation in granular EMs by coupling five explicitly defined model components: first, a one-dimensional steady compaction-shock model that maps initial solid volume fraction and shock pressure to a bulk mass-specific dissipated-work budget; second, an SEM/synthetic-image segmentation workflow that extracts pore area, perimeter, hydraulic radius, spacing, and solid volume fraction; third, stochastic Dissipation Localization Elements (DLEs) that distribute the conserved shock-dissipation budget into an image-conditioned heterogeneous temperature surrogate; fourth, an ignition-burn time-of-arrival model that decouples local Arrhenius induction time from pressure-dependent deflagration-front travel time; and fifth, a first-passage percolation analog that defines the topology-based critical timescale as the earliest time at which the reacted sublevel set contains a connected pathway across the representative analysis domain. This framework establishes a foundational methodology for converting image-derived microstructure, imposed shock loading, ignition timing, and burn-front connectivity into ensemble criticality curves. The results show that microstructure-to-microstructure variability can dominate stochastic criticality thresholds, that porosity and pore-size distributions alter criticality through both hot-spot intensity and network connectivity, and that thermal conduction primarily shifts the lower-pressure ignition branch by quenching marginal hot spots. The model qualitatively reproduces established experimental and mesoscale trends while retaining a deliberately reduced-order interpretation: the critical time is a comparative, topology-based onset metric for sustained connected reaction, not a pointwise prediction of an experimentally unique go/no-go threshold. Overall, this work demonstrates that shock-compaction dissipated work can serve as a physically constrained temperature surrogate for rapid ignition-burn analysis and that a single representative microstructure is insufficient for uncertainty-aware sensitivity prediction. The framework provides an extensible basis for future studies involving improved segmentation, finite shock-transit effects, temperature-dependent material properties, anisotropic burn propagation, three-dimensional microstructures, and additional EM formulations.

Date

7-15-2026

Committee Chair

Gonthier, Keith A.

LSU Acknowledgement

1

LSU Accessibility Acknowledgment

1

Download

Share

COinS