###### Abstract  
This work presents a three-dimensional (3D) surface-to-surface contact algorithm for SPH method and its application to the simulation of material failure during high velocity impact of a projectile on a ceramic plate. In the present contact algorithm, surfaces of 3D objects represented by SPH particles are reconstructed. Based on the reconstructed surfaces, a box test followed by a crossover test is employed to detect contacts between different objects, and a penalty method is employed to enforce contact conditions between contact pairs identified by contact detection. Validation examples are presented to demonstrate the accuracy and capability of the algorithm. The calculated results show that the present contact algorithm can achieve high accuracy and it is capable of handling various contact problems, including frictionless and frictional problems as well as small and significant deformation problems. The algorithm is then used to simulate the high velocity impact of a projectile on a ceramic plate. The material failure of the projectile and the ceramic plate is reproduced, and the residual velocity of the projectile is well predicted. 3D contact algorithm; surface-to-surface; SPH method; impact; material failure Article  
3D Surface-to-Surface Contact Algorithm for SPH Method and Its Application to Simulation of Impact Failure of Ceramic Plate  
[PERSON], [PERSON], K. 3 DSurface-to-Surface Contact Algorithm for SPH Method and Its Application to Simulation of Impact Failure of Ceramic Plate  
denoted by discrete boundary particles (points) without connectivity, and explicit surfaces cannot be obtained as such using the FEM. Therefore, the determination of penetration between contact objects and normal vectors at surfaces is not as convenient and accurate as that in the FEM. This creates difficulties preventing accurate contact modeling using the SPH method. Currently, the SPH method is mainly limited to large deformation contact problems in contact modeling and is not competitive for small and moderate deformation contact problems due to the lack of rigorous contact algorithms. Thus, it is of interest to develop accurate contact algorithms for the SPH method which can versatilely model both frictional and frictionless contact cases and contact cases with deformation from small to extremely large or even material failure. This will be helpful for promoting the application scope of the SPH method. During the development of the SPH method, various contact algorithms have been proposed to treat contacts. The early algorithm for the contact treatment is based on particle approximation. This algorithm takes all its particles from different objects in the calculation of particle approximation of the momentum conservation equation to deal with contact conditions. In this algorithm, contact detection is completed along with neighboring particle search. This algorithm is usually used to solve problems where materials behave as fluids, such as hypervelocity impact problems. Some researchers explored particle-to-particle contact algorithms [4; 5; 6]. These algorithms take particles as circles or spheres of a certain size and detect contacts between different objects based on distances between particles and sizes of particles. They employed the penalty method to enforce the contact conditions. They can eliminate the deficiency of virtual tensile and shear stresses of the particle approximation algorithm and can be used to simulate impact contact problems involving large deformation and material failure [7; 8]. However, particle-to-particle contact algorithms may encounter non-physical penetrations between contact objects in some cases, such as the penetration process with all contact objects suffering very intense deformations [9].