This work presents a multiscale modeling framework for predictive simulations of shock-to-detonation transition (SDT) in pressed energetic (HMX) materials. The macro-scale computations of SDT are performed using an ignition and growth (IG) model. However, unlike in the traditional semi-empirical ignition-and-growth model, which relies on empirical fits, in this work meso-scale void collapse simulations are used to supply the ignition and growth rates. This results in a macro-scale model which is sensitive to the meso-structure of the energetic material. Energy localization at the meso-scale due to hotspot ignition and growth is reflected in the shock response of the energetic material via surrogate models for ignition and growth rates. Ensembles of meso-scale reactive void collapse simulations are used to train the surrogate model using a Bayesian Kriging approach. This meso-informed Ignition and Growth (MES-IG) model is applied to perform SDT simulations of pressed HMXs with different porosity and void diameters. The computations are successfully validated against experimental pop-plots. Additionally, the critical energy for SDT is computed and the experimentally observed Ps2τs=constant relations are recovered using the MES-IG model. While the multiscale framework in this paper is applied in the context of an ignition-and-growth model, the overall surrogate model-based multiscale approach can be adapted to any macro-scale model for predicting SDT in heterogeneous energetic materials.

This work presents the procedure for constructing a machine learned surrogate model for hotspot ignition and growth rates in pressed HMX materials. A Bayesian Kriging algorithm is used to assimilate input data obtained from high-resolution meso-scale simulations. The surrogates are built by generating a sparse set of training data using reactive meso-scale simulations of void collapse by varying loading conditions and void sizes. Insights into the physics of void collapse and ignition and growth of hotspots are obtained. The criticality envelope for hotspots is obtained as the function cr = ( s , void ) where s is the imposed shock pressure and void is the void size. Criticality of hotspots is classified into the plastic collapse and hydrodynamic jetting regimes. The information obtained from the surrogate models for hotspot ignition and growth rates and the criticality envelope can be utilized in meso-informed Ignition and Growth (MES-IG) models to perform multi-scale simulations of pressed HMX materials.

The formation of hotspots due to collapse of voids leads to enhanced sensitivity of heterogeneous energetic (HE) materials. Several mechanisms of void collapse have been identified, but the regimes in which these mechanisms dominate have not been clearly delineated using scaling arguments and dimensionless parameters. This paper examines void collapse in cyclotetramethylene-tetranitramine (HMX) to demarcate regimes where plastic collapse and hydrodynamic jetting play dominant roles in influencing hotspot related sensitivity. Using scaling arguments, a criticality envelope for HMX is derived in the form Σcr=∑(Ps,Dvoid), i.e., as a function of shock pressure Ps and void size Dvoid, which are controllable design parameters. Once a critical hotspot forms, its subsequent growth displays a complex relationship to Ps and Dvoid. These complexities are explained with scaling arguments that clarify the physical mechanisms that predominate in various regimes of hotspot formation. The insights and scaling laws obtained can be useful in the design of HE materials.

SUMMARYA frictionless contact separation treatment in a sharp-interface Eulerian framework is presented to handle the general situation of high-speed impact and separation of materials. The algorithm has been developed for an established Eulerian-based Cartesian grid multimaterial flow code in which the interfaces are tracked in a sharp manner using a standard narrow-band level set approach. Boundary conditions have been applied using a modified ghost fluid method for elasto-plastic materials. The sharp-interface treatment maintains the distinct interacting interfaces without smearing the contact zone while also removing the difficulties associated with Lagrangian moving mesh entities in contact-separation situations. The algorithm has been tested and verified against experimental and numerical results for three different problems in the high strain rate regime, which involve contact, separation and sliding of materials.

Morphology and dynamics at the meso-scale play crucial roles in the overall macro-or system-scale flow of heterogeneous materials. In a multi-scale framework, closure models upscale unresolved sub-grid (mesoscale) physics and therefore encapsulate structure-property (S-P) linkages to predict performance at the macro-scale. This work establishes a route to structure-property linkage, proceeding all the way from imaged micro-structures to flow computations in one unified levelset-based framework. Levelsets are used to: 1) Define embedded geometries via image segmentation; 2) Simulate the interaction of sharp immersed boundaries with the flow field; and 3) Calculate morphological metrics to quantify structure. Meso-scale dynamics is computed to calculate sub-grid properties, i.e. closure models for momentum and energy equations. The structure-property linkage is demonstrated for two types of multi-material flows: interaction of shocks with a cloud of particles and reactive meso-mechanics of pressed energetic materials. We also present an approach to connect local morphological characteristics in a microstructure containing topologically complex features with the shock response of imaged samples of such materials. This paves the way for using geometric machine learning techniques to associate imaged morphologies with their properties.