Smooth-particle phase stability with generalized density-dependent 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 Φ_ρ=1/2∑(ρ-ρ₀)², along with their corresponding constitutive relations, provide a simple means for characterizing fluids and that special stabilization potentials, with density gradients or curvatures, such as Φ_∇ρ=1/2∑(∇ρ)², not only stabilize crystalline solid phases (or meshes) but also provide 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.