On the equivalence of Eulerian Smoothed Particle Hydrodynamics, Total Lagrangian Smoothed Particle Hydrodynamics and molecular dynamics simulations for solids

Abstract

Significant advances in nanoscale research have enabled the continuous miniaturization of devices. With the reduction in the size of the devices, it is important to identify if the continuum scale methods remain applicable to such small-scale systems. Motivated by this, the present work tries to understand the equivalence, or its lack thereof, of the continuum scale Eulerian Smoothed Particle Hydrodynamics (ESPH) and Total Lagrangian Smoothed Particle Hydrodynamics (TLSPH) with the atomistic scale molecular dynamics (MD) simulations. The equivalence is studied using four simple problems — (i) uniaxial tensile testing of a beam, (ii) stress profile in a pre-notched plate under small extension, (iii) head-on collision of two elastic rubber-like rings, and (iv) large deformation of a cantilever beam subjected to an impact at the free end. Using MD simulation data as the pseudo-experimental data, we show that both ESPH and TLSPH provide results that are qualitatively and quantitatively in agreement with the MD simulations if the properties at the continuum scale are obtained directly from the MD simulations, and the same initial conditions are chosen. The comparisons are based on the stress–strain behavior, the distribution of normal and shear stresses, the temporal evolution of the variables such as kinetic energy, etc.