The ability of predicting material failure is essential for adequate structural dimensioning in every mechanical design. For ships, and particularly for military vessels, the challenge of optimizing the toughness-to-weight ratio at the highest possible value is essential to provide agile structures that can safely withstand external forces. Exploring the case of underwater explosions, the present paper summarizes some of the fundamental mathematical relations for foreseeing the behavior of naval panels to such solicitation. A broad state-of-the-art survey links the mechanical stress-strain response of materials and the influence of local reinforcements in flexural and lateral-torsional buckling to the hydrodynamic relations that govern the propagation of pressure waves prevenient from blasts. Numerical simulation approaches used in computational modeling of underwater explosions are reviewed, focusing on Eulerian and Lagrangian fluid descriptions, Johnson-Cook and Gurson constitutive materials for naval panels, and the solving methods FEM (Finite Element Method), FVM (Finite Volume Method), BEM (Boundary Element Method), and SPH (Smooth Particle Hydrodynamics). The confrontation of experimental tests for evaluating different hull materials and constructions with formulae and virtual reproduction practices allow a wide perception of the subject from different yet interrelated points of view.
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