Dynamic response of contact-blast-loaded free metal plate: Theoretical model, experiments and numerical simulation

Metal plates are widely used in industry and civil engineering for the development of ships, vehicles, bridges, buildings, and aircraft. The deformation behavior of a blast-loaded metal plate is important for designing such protective structures. In this study, a theoretical model was proposed to describe the deformation of a blast-loaded metal plate. The plate deflection was the only displacement considered in this model. The deflection of the loaded metal plate was assumed to have a second-order distribution in the loaded plane. Based on von Karman's large deformation theory, the membrane strain and bending curvature are represented by the coefficients of the proposed deflection distribution. By applying Hamilton's principle, a group of governing equations was obtained for the distribution coefficients related to the loadings, as well as the constitutive model, which was represented by the Johnson–Cook model in the next analysis. The blast-loading was calculated using an ALE numerical scheme CFD solver, in which the metal plate was represented by a movable reflection boundary condition, and the movement of this boundary was governed by the deformation of the metal plate. The simulated result was verified by the explosion-driven experiment, and a good agreement was obtained. In addition, a series of numerical simulations was conducted on metal plates of different sizes loaded with different charges, to investigate the corresponding deformation behaviors. It was found that the deflection and driven velocity of the plate increased with an increase in the width–thickness ratio of the plate when the thickness of the explosive was fitted to 40 mm. The dimensionless deflection was almost linearly related to the width-to-thickness ratio. The driven velocity and deflection were only related to the width-to-thickness ratio of the plate when the explosive thickness and type were selected. A fitted polynomial relationship was obtained for both the driven velocity and deflection, based on the numerical results. Moreover, the analysis was conducted for the deflection and driven velocity related to the loading feature, and a polynomial linear regression related to four dimensionless values was obtained using the sklearn package of Python. The regression releases the theoretical model from the ALE CFD simulation and significantly increases prediction efficiency. Finally, the predicted results are discussed and the reliability of the regression is determined.