The nonlocal, local and mixed forms of the SPH method

From its early days the SPH method has been criticised for shortcomings namely tensile instability and consistency. Without thorough understanding of attempts were made to make classical consistent stable which resulted in local Total Lagrangian forms similar finite element method. In this paper we derived analysed a nonlocal similarity with Bazant’s imbricate continuum. addition, provides comparison discussion different including: Classical SPH, Nonlocal, Local Mixed SPH. The partition unity approach was used define following two mixed forms: Local–Nonlocal Local–Classical These intended modelling physical processes characterised effects (local constitutive equations), e.g. progressive damage failure. stabilising effect form on is inherently unstable (tensile instability), are also illustrated. stability analysis, presented appendices A B, demonstrate continuous discrete based Eulerian kernels elastic • Derivation Nonlocal formulation no instability. unity. Proposal Von Neumann analysis Stability requirements kernel function.