On the application of SPH to solid mechanics

We analyze the applicability of the smooth particle hydrodynamics (SPH) to the solution of boundary value problems involving large deformation of solids. The main focus is set on such issues as the reduction of artificial edge effects by implementing corrected kernels and their gradients, accurate and efficient computation of the deformation gradient tensor, evaluation of the internal forces from the given stress field. For demonstration purposes, a hyperelastic body of neo-Hookean type and a visco-elastic body of Maxwell type are considered; the formulation of the Maxwell material is based on the approach of Simo and Miehe (1992). For the implementation of constitutive relations efficient and robust numerical schemes are used. A solution for a series of test problems is presented. The performance of the implemented algorithms is assessed by checking the preservation of the total energy of the system. As a result, a functional combination of SPH-techniques is identified, which is suitable for problems involving large strains, rotations and displacements coupled to inelastic material behaviour. The accuracy of the SPH-computations is assessed using nonlinear FEM as a benchmark.