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 Phi rho=1/2 Sigma(rho-rho 0)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 Phi inverted Delta rho=1/2 Sigma(inverted Delta rho)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.