ADVANCES IN THE TENSILE INSTABILITY OF SMOOTHED PARTICLE HYDRODYNAMICS APPLIED TO SOLID DYNAMICS

SPH(smoothed particle hydrodynamics)is a gridless Lagrangian numerical method based on kernel approximation.In this method,the continuum equations of fluid dynamics are replaced by particle equations. SPH can deal with large deformation and extensive tangling,which are difficult to be handled in FEM,as well as free surface and material interface,which are tricky problems in FDM.SPH is robust in the simulation of impact,explosion and crack.However,the tensile instability is its biggest drawback in the applications to solid dynamics.Von Neumann stability analysis shows that the criterion for stability or instability can be expressed in terms of the stress state and the second derivative of the kernel function.At present,SPH tensile instability is alleviated in the stress point method,artificial stress method,CSPM(corrected smoothed particle hydrodynamics method),conservative smoothing method and other methods,but they can not completely overcome SPH tensile instability.In this paper,the theory of SPH and the idea of Von Neumann stability analysis are introduced,and the research results and recent advances in SPH tensile instability are analyzed. The existing problems and future trends in these fields are discussed.