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Highlights • The typical trapezoid-shaped back-spall becomes an oval-shaped debris cloud finally. • There are three stages: the growth, the separation and the complete breakaway. • Special particle distributions and symmetric boundary can reduce time computation. • The Kernel Gradient Correction and fixed boundary can increase the accuracy. • An obvious slope in the inner fragments of the spall can be explained by gravity. Abstract Back-spalling of ceramic plates subjected to an impact is often observed phenomena, and a better understanding of back-spalling is critical for the design of protection systems. Numerical modeling is an effective means for modeling of structural failure caused by impacts. Among many numerical methods, Smoothed particle hydrodynamics (SPH) has advantages in handling these types of problems due to its features of meshfree, Lagrangian and particle. In this study, an experiment of Φ4.8 mm steel sphere impacting on an Al 2 O 3 ceramics plate at a speed of 767 m/s is performed. A high-speed camera is used to record the spalls ejected from the back side of the plate during frontal impacts. It is observed that the spall is typically trapezoid-shaped. To study the detailed process of the spalling and the formation of the shape of the back spall, a three-dimensional (3D) SPH is developed using the JC and JH-2 constitutive models. By analyzing some feature points and lengths and the outline of the experimental and numerical spall, it is found that the spalling process can be divided into 3 major stages during the impact event time of 55μs to 445μs: the growth of spall, the separation of spall from plate, and the complete breakaway of the spall from plate. It is also observed in the simulation that the z-component velocity of the lateral side is bigger than the that of the front arc salient. This difference would finally lead the spall to become an oval-shaped debris cloud, which is the same as showed in the experiment. Some typical cracks occur and propagate within the numerical model of the ceramic plate. In the present SPH code, variable space particle distributions are applied to reduce the computation time; and the Kernel Gradient Correction (KGC) is applied to increase the accuracy. The gravity field is considered in our SPH code to simulate the slope in the trajectory of the inner fragments of the spall, which is also observed in the experiment. These improvements in SPH lead to better agreement with the experimental observations on the spall features. [ABSTRACT FROM AUTHOR]