Shock Waves

pp 1–22 | Cite as

Modeling mesoscale energy localization in shocked HMX, part I: machine-learned surrogate models for the effects of loading and void sizes

  • A. Nassar
  • N. K. Rai
  • O. Sen
  • H. S. UdaykumarEmail author
Original Article


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


Multi-scale modeling Machine learning Surrogate modeling Pressed HMX Void collapse Ignition/growth reaction rates Energetic materials 



The authors gratefully acknowledge the financial support from the Air Force Office of Scientific Research (Dynamic Materials Program, program manager: Martin Schmidt) under Grant Number FA9550-15-1-0332 and Eglin AFB, AFRL-RWPC (program manager: Angela Diggs) under the Contract Number FA8651-16-1-0005. The authors are also thankful to K.K. Choi at the University of Iowa and Nicholas J. Gaul at RAMDO LLC, Iowa City, for providing the computational code for the modified Bayesian kriging method.


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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Mechanical and Industrial EngineeringThe University of IowaIowa CityUSA

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