Ensemble-Based Data Assimilation for Material Model Characterization in High-Velocity Impact

TL;DR

This work tackles the challenge of calibrating multi-physics material models for high-velocity impact (HVI) from a single test. It proposes an ensemble Kalman filter (EnKF) data-assimilation framework that non-intrusively couples Smoothed Particle Hydrodynamics (SPH) forward simulations with augmented parameter states for Johnson-Cook plasticity, Johnson-Cook fracture, and Mie-Grüneisen EOS, using time-series back-face deflection observations and adaptive covariance inflation. Numerical experiments with synthetic AZ31B plate data show that the framework rapidly recovers sensitive parameters (notably $C$ and $\gamma_0$) within a few iterations when data are rich, while insensitive parameters (e.g., $D_4$) remain poorly identified, underscoring the importance of parameter sensitivity and information content. The study also demonstrates the method’s robustness to moderate observational incompleteness and to substantial prior misspecification, albeit with a drift-then-stall tendency when priors are extreme, and it emphasizes using ensemble spread as a diagnostic of calibration quality. Overall, the EnKF inversion offers a robust, efficient path to uncertainty-aware calibration of HVI material models directly from a single experiment, with clear guidance on data requirements and observability needs, and it sets the stage for extensions to surrogate models and heteroskedastic noise modeling.

Abstract

High-fidelity simulations are essential for understanding and predicting the behavior of materials under high-velocity impact (HVI) in both fundamental research and practical applications. However, their accuracy relies on material models and parameters that are traditionally obtained through manual fitting to multiple time- and labor-intensive experiments. This study presents an ensemble-based data assimilation (DA) framework to automatically and simultaneously calibrate plasticity, fracture, and equation of state (EOS) parameters from a single HVI test. The framework integrates Smoothed Particle Hydrodynamics for HVI simulations, the ensemble Kalman filter (EnKF) for parameter refinement, and adaptive covariance inflation to mitigate uncertainty underestimation. The approach is demonstrated using synthetic back-face deflection data from an AZ31B magnesium plate to identify Johnson-Cook plasticity/fracture and Mie-Gruneisen EOS parameters. Test cases with biased initial guesses and limited data show the EnKF-based framework accurately recovers sensitive parameters in few iterations, indicated by a convergent ensemble standard deviation. Conversely, insensitive parameters converge to incorrect values with persistently large standard deviations. Limited observational data can still achieve convergence but requires more iterations. Under extreme prior bias, sensitive parameters may exhibit a drift-then-stall behavior with small residual biases. In practice, the ensemble standard deviation thus provides a diagnostic tool to assess parameter sensitivity and calibration accuracy. This study demonstrates the proposed DA framework is a robust and efficient tool for HVI material model characterization.

Figures (10)

• Figure 1: Schematic illustration of the SPH model of the HVI problem with half the geometry hidden: (a) Initial state $t=0~\upmu\rm{s}$, and (b) Termination state $t=20.0~\upmu\rm{s}$. Red and green markers represent SPH particles of the projectile and the plate, respectively
• Figure 2: Numerical simulation results. (a) Maximum principal stress contours of the target plate. (b) Temperature field contours of the target plate.
• Figure 3: Node set selected for observation in the numerical experiment, highlighted by inverted red triangles: (a) side view, and (b) back view. Red and green markers represent SPH particles of the projectile and the plate, respectively.
• Figure 4: RMSD of back-face deflection computed at (a) $t = 10.0\,\upmu\rm{s}$, (b) $t = 11.0\,\upmu\rm{s}$, and (c) $t = 12.0\,\upmu\rm{s}$.
• Figure 5: Back-face deflection profiles produced by the extreme perturbations $\theta_i^{-}=0.75\,\theta_i$ (dashed) and $\theta_i^{+}=1.25\,\theta_i$ (solid) of the retained parameters: a) $C$, (b) $D_4$, and (c) $\gamma_0$. Curves are colored by time, red: $t = 10.0\,\upmu\rm{s}$; green: $t = 11.0\,\upmu\rm{s}$; blue: $t = 12.0\,\upmu\rm{s}$.