PSI - Issue 71

Deepu Kumar Singh et al. / Procedia Structural Integrity 71 (2025) 164–171

167

a perfectly rigid body, which is defined by the keyword MAT_020_RIGID. For the smooth interaction between sheet and projectile ERODING_SURFACE_TO_SURFACE keyword and SPC_SET boundary condition were used. Eroding surface to surface contact was used between projectile and target with friction coefficient of 0.2. The mechanical properties of natural rubber and projectile used for the material model are reported in Table 1. Table-1. Value of material parameter for rubber sheet and projectile damage model. S. No. Parameters Notation Unit Value For Natural Rubber Sheet 1 Density ρ 3 1060 2 Poisson’s Ratio ν --- 0.45 3 MR Model Constant 1 2 GPa 2 2 . . 0 5 4 2 For Hemispherical projectile 4 Density ρ 3 7830 5 Poisson’s Ratio ν --- 0.30 6 Young’s Modulus E GPa 210 3. Results and discussions Numerical simulations of conical-nosed projectile impact over natural rubber sheets under the three different thicknesses of 5 mm, 10 mm, 15 mm were carried out on LS-DYNA/ANSYS. The conical profile projectile was impacted on different thicknesses of 100 mm × 100 mm sheet under the velocities range of 150 to 350 m/s. The ballistic performance of the sheet at these impact velocities was discussed in this section. Numerical results based on the Mooney-Rivlin damage model were validated against the existing numerical results based Neo-Hookean damage model in literature (Sangamesh et al., 2018). The two material parameters-based Mooney-Rivlin material model is well defined for the nonlinear deformation behaviour of rubber sheets under ballistic impact. Table 2 shows the value of different residual velocities of the projectile for the different rubber thickness of 5 mm,10 mm, and 15 mm. Figures 2,3 and 4 show the comparison of residual velocities results obtained from NH damage model and MR damage model. From Figures 2, 3, and 4, a close correlation can be observed between the results obtained on Ls-Dyna and with numerical results based on the literature (Sangamesh et al., 2018). Hence the numerical results obtained from the Mooney-Rivlin damage model show a good correlation with the Neo-Hookean damage model. The error percentage difference between the Neo-Hookean material model and the Mooney-Rivlin model lies under 3%. The obtained results from the Mooney-Rivlin damage model in terms of residual velocity, energy absorption, and ballistic limit are obtained from the fixed set of material parameters. The penetration process of the projectile during the impact shot also reported in Fig. 5. In the damage pattern morphology, the back face signature also had close similarity with literature results (Sangamesh et al., 2018), which is shown in Fig. 6. Table-2 Parameters obtained at different impact velocities of the projectile for different thickness. Sr. No. Impact velocity (m/s) Error value (%) Residual kinetic Error value (%)

Residual velocity (m/s) (Sangames h et al., 2018)

Residual velocity (m/s) (This study)

Residual kinetic energy (J) (This study)

energy (J) (Sangames h et al., 2018)

For 5 mm thickness

1 2 3 4

350 250 150 135

234.4

235.5 124.8

0.4

137.3

138.7

1 2

126

1

39.7

38.9

54

53.2

1.5

7.3

7.1

2.8

0

0

-

0

0

-

For 10 mm thickness