On the correction of the boundary deficiency in SPH for the frictional contact simulation

Smoothed particle hydrodynamics(SPH)is a mesh-free method which is powerful for large deformation computation of soils.However,the algorithm for the simulation of frictional contact which is common in geotechnical engineering is still quite immature due to the boundary deficiency.In this study,the cause of boundary deficiency in the SPH simulation for frictional contact is analysed.Then,based on mathematical derivation,the method to correct boundary deficiency related to frictional contact is discussed theoretically,where the frictional contact algorithm is established by dividing the computational domain into several subdomains according to the existing contact boundaries and by using contact forces as bridges of these subdomains to fulfil problem solving,and the value of correction coefficient is obtained by comparing the SPH outcome of the contact particles with that calculated through Newton’s second law of motion.At the same time,from the perspective of numerical computation,an optimized value for the correction coefficient is proposed,and a thorough investigation is performed on the cubic spline kernel function and quintic spline kernel function,whose correction coefficients are found to be 2.0 and[2.0,2.16],respectively.Finally,numerical tests are carried out to verify the proposed method.The outcome of the study is helpful to providing theoretical support for the research of frictional contact simulation within the framework of SPH.