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• Underwater explosion induced cavitation near sacrificial coatings are studied. • RKDG-FE-GFM-IsenCav is developed to study the cavitation effects. • Five benchmark problems are studied. • Effects of geometrical and physical properties of the model are discussed. The load resulting from cavitation collapse is a major threat to structures exposed to underwater explosions. Protective structures for warships, such as sacrificial coatings, which are sandwich structures attached to the wet face of the ship hull. They have energy absorbing cores made of cellular or composite materials that can significantly influence the effects of cavitation. In this study, a physical model consisting of water, an explosion bubble, and a sacrificial coating is established to investigate the effects of cavitation near sacrificial coatings subjected to underwater explosions. A numerical method is developed that couples the Runge-Kutta discontinuous Galerkin method, the finite element method, a Ghost Fluid Method-based numerical technique, and an isentropic one-fluid cavitation model to capture the physical phenomena of shock wave propagation, cavitation inception, expansion and collapse, and explosion bubble expansion and contraction. To ensure the accuracy of the mathematical model, five benchmark problems and a convergence test of the numerical solution are studied. The study comprehensively discusses the influences of core strengths, face sheet thickness, stand-off distances, and structure curvature on the evolution of the cavitation region, pressure profiles near the structure, and structure responses. [ABSTRACT FROM AUTHOR]

A numerical procedure that couples the Runge–Kutta discontinuous Galerkin method (RKDG), the boundary element method (BEM) and the finite element method (FEM) is developed to study the dynamics of an underwater explosion bubble near a sandwich structure efficiently and accurately. The numerical approach is validated by a near-field underwater explosion experiment. The numerical predicted bubble shape, cavitation and the free field pressure are in good agreement with the experimental results. The validated code is then used to determine the effects of the foam core strengths, the stand-off distances and the boundary condition of the back face sheet on the fluid response, the bubble behaviors, and the deformation of the sandwich structure. The results are beneficial for guiding the design of the protection structures. • Dynamics of an underwater explosion bubble near a sandwich structure is studied. • A numerical procedure that couples RKDG, BEM and FEM is developed. • Deformation of sandwich structures has significant effects on the bubble behaviors. [ABSTRACT FROM AUTHOR]

The dynamics of an underwater explosion bubble interacting with a moveable plate with basic characteristics of a sandwich structure are investigated numerically using boundary element method. The response of sandwich structures is assumed to be a moveable plate with a given velocity profile. The influence of the plate velocity profile, the standoff distance and the scale of the plate on the bubble behaviors are discussed. Within the scope of discussions, the bubble volume and period are a decreasing function of the maximum crushing velocity, the core compression, and the plate dimension, and an increasing function of the standoff distance. Three different regimes of bubble behaviors are distinguished: (1) jet directing towards the plate; (2) the bubble splitting into multiple bubbles or oscillating spherically without jet; (3) jet directing away from the plate. The results indicate that the sandwich plate which can provide larger deformation and larger maximum deformation velocity is beneficial for altering the jet direction to direct away from the plate. [ABSTRACT FROM AUTHOR]

The cellular materials are well known to mitigate shock loadings. However, they may attenuate or enhance the shock transmitted to the protected structures. This paper is devoted to derive an explicit expression of the effective foam thickness when subjected to deep underwater explosion. Hereinafter, the effective foam thickness represents the crushed foam when the shock energy is just completely absorbed, i.e. the attenuation/enhancement boundary. One-dimensional (1D) analytical model which can consider the core crushing, the fluid-structure interaction (FSI), the cavitation phenomenon and the initially applied static pressure is proposed to solve the problem. The analytical model is then used for the parametric study. Finally, the empirical formulae of the effective foam thickness is derived from the results of the parametric study. In practical applications, the empirical formulae for the effective foam thickness can guide the design of such cellular claddings to water blast. [ABSTRACT FROM AUTHOR]

A numerical solver coupling the Runge-Kutta discontinuous Galerkin method to the finite element method is proposed to solve the two-dimensional (2D) or axisymmetric response of deformable sandwich structures with metallic foam cores subjected to underwater explosion, in which the interactions of the gas bubble, the shock wave, the sandwich structure and cavitation are taken into account. The coupling method combines the advantages of the ghost fluid method (GFM) and the modified ghost fluid method (MGFM), where the Lagrangian interface velocity is directly set as the solution of the Riemann problem and the interface pressure and the fluid density are obtained by solving the Riemann problem (with the pre-known interface velocity). The obtained interface pressure then serves as the boundary condition to the Lagrangian domain. For the Eulerian domain, the remaining procedure is similar to the MGFM. The method proposed in this paper is material independent in simulating the fluid-structure interaction which is its major advantage compared with the original MGFM. The method is successfully validated by using analytical, numerical, and experimental results. [ABSTRACT FROM AUTHOR]

A fluid model is developed and used in combination with Abaqus/Explicit to investigate the effects of graded foam cores on the loading of a sandwich spherical shell subject to underwater explosion from the inner side, after having validated the modeling technique by reproducing results by other authors. Based on the relation between the core strength and the stiffness of the outer face sheet (OFS), four different situations are considered to discuss the graded effects. It is demonstrated that for the case of relatively strong cores and the OFS with low stiffness or soft cores and the OFS with high stiffness, the core arrangement of low/medium/high (relative density from the inside to the outside) has the best performance to shock loadings which is a consequence of the effects of the fluid–structure interaction and the energy absorption capability; on the other hand, for the case of intermediate core strengths and stiffness of the OFS where the pulling-back force due to the stretching of the OFS is close to the core strength, the configuration of high/medium/low has the best performance due to its higher energy absorption efficiency of the foam and lower transmitted stress. [ABSTRACT FROM AUTHOR]

Underwater explosion seriously affects the combat performance and vitality of submarines. In order to improve the blast resistance of stiffened double cylindrical shells, a new type of stiffened style that replaces the traditional T-shaped stiffeners with circular tube stiffeners, namely O-shaped stiffeners are studied. A series of comparative underwater explosion tests are carried out on two scaled stiffened double cylindrical shells with O and T-shaped stiffeners. Based on the tests, more detailed numerical simulations are made to explore the influence of the structure parameters on the shock performance of the whole structure. It is shown that the O-shaped stiffeners show more superior crushing performance than T-shaped ones when the large plastic deformation appears on the shells. As the plastic deformation of the T-shaped stiffeners is dominated by harmonic buckling while that of the O-shaped stiffeners is dominated by the flattening deformation of circular tubes, the latter can produce greater plastic deformation and absorb more shock energy to reduce the internal energy of pressure hull and thin hull. The shock response spectrums measuring at pressure hull can also be significantly attenuated at high frequency band. Therefore, the O-shaped stiffeners may be more effective sacrificial connected structures in the submarine. • Circular tube is proposed as the stiffener of double cylindrical shells to improve the blast resistance. • Comparative non-contact underwater explosion tests are carried out on the stiffened double cylindrical shells. • The circular tube stiffeners are effective sacrificial connected structures to protect the inner and outer hull. [ABSTRACT FROM AUTHOR]

• This work deals with the shock mitigation effects of sacrificial coatings plastered on the stiffened double cylindrical shell. • The physical experiments of a stiffened double cylindrical shell under non-contact underwater explosion are carried out. • The coating on the thin hull plays the key role to mitigate shock loadings while the coating on the pressure hull has limited effects. Underwater explosion shock loadings can seriously damage the vitality and fighting capacity of warships. Plastering a layer of sacrificial coating on the ship hull is one of effective strategies to isolate shock impulses and absorb shock energy. In this paper, the shock mitigation effects of sacrificial coatings plastered on a stiffened double cylindrical shell are analyzed numerically. The numerical models are validated by conducting a series of physical experiments of a stiffened double cylindrical shell under noncontact underwater explosion. Three different configurations are considered: both the pressure and thin hulls are plastered with sacrificial coatings; only the thin hull is plastered with sacrificial coatings; and only the pressure hull is plastered with sacrificial coatings. The total pressure field in water and the dynamic response of the stiffened double cylindrical shell are obtained. The results indicate that the deformation and motion of the sacrificial coatings can more easily generate rarefaction wave, which can decrease the total shock impulse acting on the structure. Among three configurations, the configuration of the coating plastered on the thin hull has a better capability of isolating the shock impulse and reducing the shock loadings transmitted to the pressure hull. The dynamic stress and velocity responses of the shell are effectively decreased. Comparisons between different configurations suggest that the coating on the thin hull plays a key role in mitigating shock loadings, while the coating on the pressure hull has limited effects. Moreover, comparison results between the bare hull and the equivalent model which increases the thickness of the thin or pressure hulls under the same mass conditions indicate that the method of using a sacrificial coating is more effective in improving the blast resistance of the structure. The research results are useful in guiding the shock resistance design of stiffened double cylindrical shells. [ABSTRACT FROM AUTHOR]

Underwater explosions can cause significant damage to ship structures, and quickly assessing the extent of the damage is crucial for improving warship combat capability. This paper proposes the use of machine learning algorithms to rapidly assess the damage of stiffened plates subjected to underwater explosions. The algorithms use structural responses of the plates obtained by numerical simulations, which are benchmarked by experimental results, as a database. Fractures and plastic deformations are both taken into consideration. The support vector machine algorithm is used to determine the criterion for fractures or plastic deformations, while a back propagation neural network model and a support vector regression model are both used to predict the plastic deformation and fracture area of the plates. The support vector machine model accurately classified different cases of fractures or plastic deformation with a training accuracy of 99.4%. The back propagation neural network model has regression values of 0.99 for predicting fractures and 0.97 for predicting plastic deformation, both of which are higher than those predicted by the support vector regression model (0.96 for the prediction of fracture and 0.90 for the prediction of plastic deformation). Therefore, the back propagation neural network model provides a more accurate assessment of damage to stiffened plates subjected to underwater explosions and can be used for rapid assessment. • Machine learning algorithms are employed to predict the structural response. • The responses of stiffened plates subjected to underwater explosions are studied. • The criterion for fractures or plastic deformations is determine by the SVM model. • The BP neural network model and the SVR model are compared. • Rapid assessment of fractures or plastic deformation can be achieved. [ABSTRACT FROM AUTHOR]

• A eulerian compressible fluid model combines the isentropic single fluid model to solve shock wave propagation and water cavitation of water-filled double plate model. • A freestanding or softly supported outer plate has a minimal effect on the impulse transmitted to the inner plate and its motion. • Stiff support spring of the outer plate can reduce the shock wave transmitted to the gap water and also the motion of the inner plate. • Cavitation initiates in gap water near the inner plate and spreads towards the external water. • Stiff support spring of the inner plate will suppress water cavitation. Water-filled double hulls are a prevalent design for underwater warships. Studying the propagation of underwater shock wave in such structures is essential to comprehend their shock resistance. The aim of this paper is to investigate the propagation of underwater shock wave and water cavitation in a water-filled double plate. To achieve this objective, the paper establishes a Eulerian compressible fluid model that combines the isentropic single fluid model and Newton's second law. The accuracy of the numerical solver is confirmed through validation tests. The reflection and transmission characteristics of shock wave, the dynamic response of the plate, and the cavitation in external and gap water are analyzed. It also examines the effects of the supporting springs of outer and inner plates and the area density of the outer plate on the shock wave propagation and cavitation evolution. The findings indicate that the transmitted wave in the gap water is influenced by the area density and supporting spring of the outer plate. A thicker outer plate can reduce the peak value of the transmitted wave, and a stiffer supporting spring can decrease the transmitted impulse. On the other hand, if the outer plate is freestanding or softly supported, it has minimal effects on the response of the inner plate. Moreover, the water cavitation is determined by the supporting spring of the inner plate in the case of a softly supported outer plate, and the cavitation initially develops in the gap water near the inner plate before expanding towards the external water. When the supporting spring of the outer plate is stiff, it significantly reduces the occurrence of cavitation in the external water, while the cavitation in the gap water is still determined by the support spring of the inner plate. These research findings are valuable for analyzing the shock resistance of typical double-hull submarines. [Display omitted] [ABSTRACT FROM AUTHOR]

Near-field underwater explosions can cause serious local damage to ship hulls. A protective shield sticking on the outer surface of a ship hull can effectively attenuate the shock loadings from these explosions. The present paper aims to experimentally and numerically analyze the anti-shock effects of a protective shield, which consists of rigid polyurethane foam (R–PUF) with certain thickness, and thin rubber skin, coated onto a circular plate in a near-field underwater explosion. The underwater explosion experiment was conducted in a man-made lake for both the bare and coated circular plates. The experimental results indicate that the protective shield can reduce the overall deformation of the circular plate by 41.1% on average under the experimental conditions. Then a Eulerian compressible fluid model is developed and used in combination with Abaqus/Explicit software in a numerical simulation to explore the anti-shock effects of protective shields. The overall deformation, velocity and displacement of the circular plate, and the pressure and velocity of the fluid are calculated. Comparisons between the experimental results and numerical simulations indicate that the developed compressible fluid model can effectively calculate the fluid response and the overall deformation of the circular plate effectively. The simulated results illustrate that the protective shield can effectively mitigate the peak value and the duration of pressure on the wetted surface in the initial stage. Then, two situations are considered to deeply investigate the shock mitigation effects of the protective shield. When the protective shield is kept unchanged while the detonation distance is changed (situation I), it was found that softer protective shields are needed for far detonation distance while stronger protective shields are needed for near detonation distance. Moreover, when the shock environment remains unchanged and the mechanical properties of the protective shield are changed (situation II), it was found that the protective shield should be as soft as possible to generate a sufficient energy absorption capacity. These research results are useful in protective shield design for ship hulls subjected to near-field underwater explosions. • The anti-shock effects of rigid polyurethane foam to near-field underwater explosion are analyzed. • A compressible fluid model is developed to solve the near-field underwater explosion problem. • The matching between the strength of the protective shield and the shock environment has significant influences on the anti-shock effects. [ABSTRACT FROM AUTHOR]