Smooth-Particle Phase Stability with density and density-gradient potentials

Stable fluid and solid particle phases are essential to the simulation of continuum fluids and solids using Smooth Particle Applied Mechanics. We show that density-dependent potentials, such as Phi=(1/2)Sum (rho-rho_0)^2, along with their corresponding constitutive relations, provide a simple means for characterizing fluids and that a special stabilization potential, Phi=(1/2)Sum (delrho)^2, not only stabilizes crystalline solid phases (or meshes) but also provides a surface tension which is missing in the usual density-dependent-potential approach. We illustrate these ideas for two-dimensional square, triangular, and hexagonal lattices.