Evaluation of accuracy and stability of the classical SPH method under uniaxial compression

The accuracy and stability of the classical formulation of the smoothed particle hydrodynamics (SPH) method for modelling compression of elastic solids is studied to assess its suitability for predicting solid deformation. SPH has natural advantages for simulating problems involving compression of deformable solids arising from its ability to handle large deformation without re-meshing, complex free surface behaviour and tracking of multiple material interfaces. The 'classical SPH method', as originally proposed by Monaghan (in Ann Rev Astron 30:543-574, 1992, Rep Prog Phys 68:1703-1759, 2005), has become broadly established as a robust method in different areas, especially involving fluid flows. However, limited attention has been paid to understanding of its numerical performance for elastic deformation problems. To address this, we evaluate the classical SPH method to explore its stability, accuracy and convergence and the effect of numerical parameters on elastic solutions using a generic uniaxial stress test. Short term transient and long term uniform state SPH solutions agree well with those from the finite element method (FEM). The SPH elastic deformation solution showed good convergence with increasing particle resolution. The tensile instability stabilisation method was found to have little impact on the solution, except for higher values of the correction factor which then produce small amplitude benign artificial banded stress patterns. The use of artificial viscosity is able to eliminate the instability and improve the accuracy of the solutions. Overall, the classical SPH method appears to be robust and suitable for accurate modelling of elastic solids under compression.