*4.2. Linear Interpolation of Meta-Models*

In Section 3, it was proposed to interpolate linearly meta-model predictions to extend the latter to arbitrary anvil velocities. Next, in Figures 10–12, we show a comparison between the predictions of the QoI ∆*R* obtained from meta-model interpolation and full FE simulations.

**Figure 10.** Comparison of meta-models interpolated results and FEM simulations, considering ∆*R* for the Johnson–Cook model.

Observing these plots and the results collected in Table 4, we conclude that the meta-model interpolation for the Johnson–Cook and Zerilli–Armstrong models provides accurate predictions of ∆*R* for arbitrary impact velocities. In contrast, the interpolations of the Arrhenius-type model are not as accurate, possibly due to the relatively higher non-linearity of its constitutive equation, affecting directly the flow stress computation. Without a direct means of verifying this assertion, we might speculate that these non-linearities trigger complex deformation patterns in the anvil once the material enters the plastic regime. However, given that the maximum relative error is below 7 × 10 −2 in all three cases, we can accept the interpolated predictions for the three constitutive models. This choice will result in huge computational savings for the Bayesian calibration.

**Table 4.** Errors in the meta-model predictions of ∆*R* compared with full FE simulations.

**Figure 11.** Comparison of meta-models interpolated results and FEM simulation results, considering ∆*R* for the Zerilli–Armstrong model.

**Figure 12.** Comparison of meta-models interpolated results and FEM simulation results, considering ∆*R* for the Arrhenius-type model.

We have also validated the linear interpolation strategy for the quantity ∆*L*. The results are very similar to the ones obtained for ∆*R* and the interpolation plots are not presented. Table 5 collects the errors made by the meta-model for ∆*L* as compared with the FE solution, leading us to conclude, as for the previous QoI, that the interpolated predictions are accurate enough.


**Table 5.** Errors in the meta-model predictions of ∆*L* compared with full FE simulations.
