Sensitivity Analysis and Bayesian Calibration of a Holmquist-Johnson-Cook Material Model for Cellular Concrete Subjected to Impact Loading

Abstract

Periodic updates to small caliber weapon systems and projectiles used in military and law enforcement have resulted in consistently increasing material penetration capabilities. With each new generation, ballistics technology outpaces the lifecycle replacement of live-fire training facilities. For this reason, it is necessary to develop and maintain constitutive material models for use in analyzing the effects new threats will have on existing facilities and for designing new training facilities using numerical methods. This project utilizes material testing data to characterize cellular concretes used in the construction of live-fire training facilities with a 13-parameter Holmquist-Johnson-Cook (HJC) concrete constitutive model. Various statistical tools are used in this analysis to successfully describe the importance of each model parameter and quantify their uncertainty. First, Bayesian linear regression was used to calibrate the parameters in the strength and pressure components of the HJC material model given testing data of cellular concrete. These uncertain parameters were then used to construct computer simulations of penetration and perforation experiments that were previously conducted by Collard and Lanham. Then, Latin Hypercube Sampling of the parameter space was used to generate training data for a Gaussian Process surrogate model of the computer simulation. Using the surrogate model, a global variance-based sensitivity analysis of the material model was completed by computing main and total effect Sobol indices. Finally, a Bayesian calibration of the computer simulation based on the physical experiments was conducted to fully characterize the stochastic behavior of the material subjected to perforation impacts. These approaches can be used to inform decision makers about the potential risk associated with existing facilities and by designers of future live fire training facilities.