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Accurate simulations of the shock response of heterogeneous energetic (HE) materials require closure models, which account for energy localization in the micro-structure. In a multi-scale framework, closure is provided by reaction rate models that account for ignition and growth of hotspots, allowing for prediction of the overall macro-scale sensitivity of a HE material. In the present meso-informed ignition and growth (MES-IG) model, the reaction rate is expressed as a function of shock pressure and morphology of the void field in a pressed energetic material. In MES-IG, the void morphology is quantified in terms of a limited number of parameters: viz., overall porosity, void size, and shape (aspect ratio and orientation). In this paper, we quantify the effects of arbitrary variations in void shapes on meso-scale energy deposition rates. A collection of voids of arbitrary shapes is extracted from scanning electron microscope (SEM) images of real, pressed HMX (octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine) samples and classified into groups based on their similarity in shapes. Direct numerical simulations (DNS) are performed on the highly contorted "real" void shapes, and the calculated hotspot ignition and growth rates are compared with values predicted by the MES-IG. It is found that while the parameterization of complex void morphologies in terms of orientation and aspect ratio gives fairly good agreement between DNS and MES-IG reaction rates, the intricate details of highly complex void shapes impact hotspot characteristics to a significant extent. This work suggests possible improvements for the prediction of reaction rate in the energetic microstructure by adopting a more detailed description of shapes. [ABSTRACT FROM AUTHOR]

Predictive simulations of shock-to-detonation transitions (SDTs) of energetic materials must contend with uncertainties in the material properties, reactive models, and the microstructures of the material. In this work, we analyze the effects of uncertainties in the run-to-detonation distance h of a pressed energetic (HMX) material due to variabilities in the thermomechanical properties of HMX. The run distances are computed using a recently developed machine-learning based multiscale modeling framework, viz., the Meso-informed Ignition and Growth (MES-IG) model. The input uncertainties are first used in the MES-IG model to quantify the variabilities in the hotspot dynamics at the mesoscale. A Kriging-based Monte Carlo method is used to construct probability density functions (pdfs) for the mesoscale reaction-product formation rates; these are used to propagate the mesoscale uncertainties to the macroscale reaction-progress variables to construct pdfs for the run-to-detonation distance h. We evaluate uncertainties in h due to variabilities in six material properties, viz., specific heat, Grüneisen parameter, bulk modulus, yield strength, thermal expansion coefficient, and the thermal conductivity of the material. Among these six properties, h is found to be most sensitive to the variabilities in the specific heat of the material; the uncertainties in the specific heat amplify exponentially across scales and result in logarithmic pdfs for h. Thus, the paper not only quantifies and propagates uncertainties in material properties across scales in a multiscale model of SDT, but also ranks the properties with respect to the sensitivity of the SDT response of heterogeneous energetic materials on each property. [ABSTRACT FROM AUTHOR]

Meta- (or surrogate-) models constructed from meso-scale simulations can be used in place of empirical correlations to close macro-scale equations. In shocked particulate flows, surrogate models for drag are constructed as functions of shock Mach number ( Ma ), particle volume fraction ( ϕ ), Reynolds number ( Re ), etc. The computational cost of the high-fidelity meso-scale simulations is a challenge in construction of surrogates in such hierarchical multi-scale frameworks. Here multifidelity surrogate-modeling techniques are evaluated as inexpensive alternatives to high-fidelity surrogate models for obtaining closure laws for drag in shock–particle interactions. Preliminary surrogates for drag as a function of Ma and ϕ are constructed from ensembles of low-fidelity (coarse grid) mesoscale computations. The low-fidelity surrogates are subsequently corrected using only a few ( N h f ) high-fidelity computations to obtain multifidelity surrogate models. The paper evaluates three different methods for correcting an initial low-fidelity surrogate; Space Mapping (SM), Radial Basis Functions (RBF) and Modified Bayesian Kriging (MBKG). Of these methods, MBKG is found to provide the best multi-fidelity surrogate model, simultaneously minimizing the computational cost and error in the constructed surrogate. [ABSTRACT FROM AUTHOR]

The effectiveness of several metamodeling techniques, viz. the Polynomial Stochastic Collocation method, Adaptive Stochastic Collocation method, a Radial Basis Function Neural Network, a Kriging Method and a Dynamic Kriging Method is evaluated. This is done with the express purpose of using metamodels to bridge scales between micro- and macro-scale models in a multi-scale multimaterial simulation. The rate of convergence of the error when used to reconstruct hypersurfaces of known functions is studied. For sufficiently large number of training points, Stochastic Collocation methods generally converge faster than the other metamodeling techniques, while the DKG method converges faster when the number of input points is less than 100 in a two-dimensional parameter space. Because the input points correspond to computationally expensive micro/meso-scale computations, the DKG is favored for bridging scales in a multi-scale solver. [ABSTRACT FROM AUTHOR]