# Dynamic Response of Copper Plates Subjected to Underwater Impulsive Loading
## 1 Introduction  
Flat-panel structures that are widely used in naval assets and warships are sometimes affected by underwater explosions (UNDEX) because of, for example, torpedo attacks [1]. In the design and application of ships, small curvature hull panels with welded stiffeners can be considered flat-panels [2]. Currently, experimental and computational methods have been used to investigate the dynamic response of plate structures with different geometric dimensions and materials. However, the response of these structures to dynamic loading is not well understood. Due to high deformation rates and their corresponding short loading times and material nonlinearity, the structural dynamic response caused by an UNDEX is complex. Hence, it is difficult to accurately measure deformation fields in the dynamic response of a metal plate subjected to underwater impulsive loading. The material response to different loading rates has been examined through shock loading experiments. [PERSON] et al. experimentally studied the large deformation behavior of hull panels subjected to an UNDEX [3]. [PERSON] et al. investigated the deformation and failure modes of thin rectangular plates and cylindrical shell panels through experimental and numerical methods [4; 5; 6]. The results showed that the pressure on the plate is approximated by [PERSON]'s empirical formula and [PERSON]'s plate theory [7; 8]. [PERSON] et al. carried out studies on aluminum alloy plate underwaterblast loading, and further measured the underwater pressure, acceleration, and strain histories on the plate [9]. Experimental measurements are affected by some uncertainties (pressure reflections, vibrations, etc.) because of the complex and hazardous nature of UNDEX, and therefore many experimental apparatuses incorporating fluid-structure interaction (FSI) effects have been developed. In recent years, a cylinder-shaped underwater shock simulator, in lieu of explosive detonation, was utilized by [PERSON] et al. to produce shock loading on stainless steel similar to the loading generated in an UNDEX [10]. According to the study, the shock loading pressure generated in the water chamber can be independently controlled by changing the velocity and mass of the flyer plate. A combination of the shadow moire technique and high speed photography was used to record the full deformation fields of steel plates. [PERSON] et al. used this experiment setup to study the deformation and energy absorption performance of I Core sandwich structures [11]. [PERSON] et al. presented a similar experimental setup to investigate the effect of panel thickness on the dynamic response of composite sandwich plates [12]. A similar equivalent device was also designed by [PERSON] et al. to load polymer-metal bilayer plates. They analyzed the influence of polymer coating and found four typical failure models [13]. With the current rapid development of the digital image correlation (DIC) method, the measurement of complex and inhomogeneous deformation fields has become relatively easy [14]. [PERSON] et al. experimentally investigated the deformation and failure mechanisms of an aluminum panel and a stationary carbon fiber reinforced polymer (CFRP) panel under transient ballistic impact. Full-field 3D deformation has been measured by a single-camera high-speed stereo-DIC technique [15]. The development of high-speed photography technology has allowed 3D full-field deformation measurements using two high-speed digital cameras. [PERSON] et al. applied a 3D DIC technique to measure the dynamic response of aluminum plates subjected to free air blast loading conditions and an explosively driven shock tube (EDST) [16; 17]. These studies showed a different structural response, a linear elastic-plastic deformation, and elastic vibration for the free air blast loading and the EDST loading, respectively. [PERSON] et al. studied the dynamic response of thin metal plates under confined air blasting loading, and measured 3D full deformation fields using the 3D DIC technique [18]. [PERSON] et al.