## 4 Numerical Analysis of EOI Test and Spalling Test  
The edge-on impact experiments performed in an open configuration were numerically simulated with the Abaqus-explicit Finite-Element code. The target, 200 mm in height, 120 mm in width, and 14 mm in thickness, is impacted by a cylindrical projectile (D20.1 \(\times\) H40) made of a high-strength aluminium alloy. The confinement system is represented by a half cylinder, 60 mm in diameter and 52 mm in length, made of high-strength steel. The half-cylinder is 1 mm shifted from the target front edge, as in the experiments. The three solids are meshed with \"C3D8R\" eight-node solid brick elements with reduced integration and a mesh size of 1 mm to 2.5 mm. The two symmetry planes associated with the problem made it possible to only analyse a quarter of the projectile-target configuration. The projectile and confinement system are modelled considering an elastic-perfectly-plastic behaviour with the parameters reported in Table 4.  
A first numerical simulation of the EOI test was conducted with the objective of analysing the stress field induced by the impact loading. To do so, the KST model was considered for the target. The parameters related to the volumetric and deviatoric responses were identified from quasi-oedometric compression tests reported in [1] (Table 4). Pressure as high as 360 MPa is observed at 4 \(\upmu\)s beneath the confinement system (Figure 10(a)). However, pressure rapidly goes down to 180 MPa at 8 \(\upmu\)s (Figure 10(b)). It can be concluded that the quasi-oedometric compression tests provided a calibration of the KST model in  
Figure 10: EOI test in the sarcophagus configuration (\(v=162\) m/s). Pictures of the target: (**a**) prior to impact and (**b**) after impact. the correct range of pressure. It is also observed that the minimum value of volumetric strain does not exceed \(-0.8\%\) beyond the confined area, which corresponds to a level of hydrostatic pressure less than 120 MPa. This matches a quite low level of compaction and shearing deformation. Therefore, in the second midsection of the target, a minimal amount of compression damage is expected. However, according to Figure 12a,b a wide field of tensile stresses spreads out the target beyond the confined area. These tensile stresses mainly correspond to hoop stresses in a cylindrical frame centred on the impact point. Given the amplitude of tensile stresses (up to 24 and 33 MPa, respectively, at 20 \(\upmu\)s and 36 \(\upmu\)s) and the range of measured strengths in 3-point bending tests (from 0.673 to 2.989 MPa), a large network of radial cracks can be expected in the absence of structural defects. This assumption is confirmed by the second numerical simulation performed in order to illustrate the potential influence of a single structural defect on the final damage pattern of the target. Two calculations, with and without a structural defect, were conducted in which the KST-DFH model was used as the constitutive model for the target. The DFH model is a micromechanical model that provides a description of the multiple fragmentation processes involved in brittle materials at high strain rates in terms of crack inception, crack propagation, and obscuration of critical defects from propagating cracks. The main DFH model parameters are, on the one hand, the parameters driving the density of critical defects. The Weibull parameters identified from 3-point bending tests are used as input in the DFH model for this purpose. On the other hand, a set of parameters driving the growth of obscuration zones is defined. The volume of obscuration zones is related to \(S\), a shape parameter, and to the crack speed that is assumed to be constant (\(V_{crack}=KC_{0}\)) where k is a dimensionless parameter and \(C_{0}\) the 1D wave speed defined in Equation (2).