PSI - Issue 71

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

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(c) Fig. 1- Geometric modeling of (a) Natural rubber sheet, (b) Arrangement of natural rubber sheet and projectile, (c) Conical shape projectile. 2.2 Constitutive modelling for projectile and rubber sheet In the ballistic impact field, when a projectile carries high impact velocity a large deformation takes place in target sheets because the generated strain rates were too high. For this type of nonlinear damage analysis, LS DYNA/ANSYS has a predefined material damage model named as a ‘Monney - Rivlin model’. This material model was used to simulate the impact response of natural rubber against a projectile. This model is defined in LS-DYNA by the keyword of MAT_027_MOONEY-RIVLIN_RUBBER. The Mooney-Rivlin constitutive equation for rubber is followed by = 1 ( 1 −3)+ 2 ( 2 −3) (1) where W is the strain energy density function, 1, and 2 are the material constants, 1 and 2 are the first and second invariants of the Cauchy-Green deformation tensor. For rubber material, due to the negligible compressibility against the applied force, the incompressibility hypothesis is often used 3 =1. Therefore, we determine that W=W ( 1 , 2 ). According to the theory of hyperelasticity, the Cauchy stress σ tensor is expressed for hyperelastic materials by = − + 2 ( 1 + 1 2 ) − 2 2 2 (2) In which ‹• the unit tensor, is the hydrostatic pressure (determined from boundary condition), B is the left Cauchy Green deformation tensor (defined as B=FF T ) and F is the deformation gradient tensor. The projectile is assumed to be