Correction and stabilization of smooth particle hydrodynamics methods with applications in metal forming simulations

Smooth particle hydrodynamics (SPH) is a robust and conceptually simple method which su ers from un- satisfactory performance due to lack of consistency. The kernel function can be corrected to enforce the consistency conditions and improve the accuracy. For simplicity in this paper the SPH method with the corrected kernel is referred to as corrected smooth particle hydrodynamics (CSPH). The numerical solutions of CSPH can be further improved by introducing an integration correction which also enables the method to pass patch tests. It is also shown that the nodal integration of this corrected SPH method su ers from spurious singular modes. This spatial instability results from under integration of the weak form, and it is treated by a least-squares stabilization procedure which is discussed in detail in Section 4. The e ects of the stabilization and improvement in the accuracy are illustrated via examples. Further, the application of CSPH method to metal-forming simulations is discussed by formulating the governing equation associated with the process. Finally, the numerical examples showing the e ectiveness of the method in simulating metal-forming problems are presented