PSI - Issue 81

Anandito Adam Pratama et al. / Procedia Structural Integrity 81 (2026) 58–65

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UNDEX triggers the sudden formation of a shock wave with a very short duration, ranging from 0.01 to 1 millisecond. This shock wave originates from the rapid decomposition of unstable explosives into stable solid and gaseous phases, accompanied by the release of a large amount of thermal energy into the surrounding water medium, as described by Nagesh and Gupta (2021). The magnitude of the released energy depends primarily on the explosive charge mass and the stand-off distance from the target. The resulting pressure decay induced by an underwater explosion acting on a submerged structural panel can be described using the formulations presented in Equations (1)-(4), as proposed by Cole and Weller (1948) and Keil (1961).     / max , 0 d t t P t P e t        (1) Where the peak pressure ( , in MPa), decay constant ( , in ms), and delay time ( , in μs) can be d etermined by the following relationships: 1 1/3 max 1 A W P K R        (2) (4) In the above equations, and are UNDEX constants whose values are shown in Table 1, as referred to in the research of Cole and Weller (1948) and Reid (1996). Then, is a time variable, is a time delay, is an explosive mass, is the stand-off distance, 0 is the normal distance of the stand-off point to the Charge, and is the sound speed in water. The resulting impulse pressure ( , in MPa.s) and total energy ( , in kJ/m 2 ) from UNDEX loading can be formulated as Equations (5) and (6).   0 I P t dt    (5)   2 0 1 E P t dt c     (6) 2 1/3 1/3 2 KW A W R         (3)   0 / R R c   d t The extent of damage caused by an explosion is generally described by the energy density of the shock wave on the structure, known as the shock factor (SF). The mass of the explosive influences this parameter ( ), the angle of incidence of the explosion ( ). A higher Shock Factor (SF) value corresponds to greater energy transmitted to the structure, making it a practical design parameter for estimating safe stand-off distances and assessing the resistance of marine structures to underwater threats, as discussed by Jen (2009) and Keil (1961). The shock factor is formulated in Equation (7) following the definitions proposed by Keil (1961) and Gupta et al. (2010). 1 cos 2 W SF R    (7) 3. Design and Material In this study, the response of sandwich panel structures to UNDEX loads was modelled using the Coupled Acoustic – Structural Analysis (CASA) method implemented in Abaqus. The UNDEX loading was represented using an incident wave – based approach, with the explosion parameters and input definitions specified according to the values summarized in Table 1. The simulation settings were explicitly configured to describe the fluid – structure interaction conditions. The sandwich panels used in this study refer to those examined by Saputra et al. (2024), who investigated sandwich panels with four cellular core configurations: S-core, U-core, X-core, and Y-core, under impact loading conditions. Corrugated or wave-like structures inspire the S-core; the U-core is Table 1. Constants for explosives in SI units, proposed by Cole and Weller (1948) and Reid (1996). Type Constant High Blast Explosive (HBX-1) Trinitrotoluene (TNT) Pentaerythritol tetranitrate (PETN) Nuclear , MPa 1 1 2 2 53.51 1.144 0.092 -0.247 52.12 1.180 56.21 1.194 0.086 -0.257 10600 1.13 , ms 0.0895 -0.185 3.627 -0.22