  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.
