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Smooth-particle phase stability with generalized density-dependent potentials.

Wm G Hoover¹, Carol G Hoover

¹Highway Contract 60, Box 565, Ruby Valley, Nevada 89833, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|February 21, 2006

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Density-dependent potentials characterize fluids, while stabilization potentials with density gradients stabilize solid phases and introduce surface tension in continuum simulations. These methods enhance smooth particle applied mechanics for fluid and solid modeling.

Area of Science:

Computational physics
Materials science
Fluid dynamics

Background:

Smooth particle applied mechanics (SPAM) requires stable fluid and solid phases for continuum simulations.
Existing methods using density-dependent potentials effectively characterize fluids but lack surface tension.
Stabilizing solid phases in SPAM is crucial for accurate simulations.

Purpose of the Study:

To introduce density-dependent potentials for characterizing fluid phases.
To develop special stabilization potentials for solid phases and introduce surface tension.
To illustrate these potential formulations for 2D lattice structures.

Main Methods:

Utilized density-dependent potentials (Phi(rho) = 1/2 Sigma((rho-rho0)^2)) to model fluid behavior.

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Employed stabilization potentials with density gradients/curvatures (Phi(∇ρ) = 1/2 Sigma((∇ρ)^2)) for solid phase stabilization and surface tension.

Applied these potentials to 2D square, triangular, and hexagonal lattices.

Main Results:

Density-dependent potentials successfully characterized fluid phases.
Stabilization potentials effectively stabilized crystalline solid phases (meshes).
The proposed stabilization potentials introduced surface tension, a feature absent in standard density-dependent potentials.

Conclusions:

A combination of density-dependent and stabilization potentials offers a comprehensive approach for simulating both fluid and solid phases.
The introduction of surface tension via stabilization potentials improves the accuracy of continuum simulations.
The demonstrated 2D lattice examples highlight the versatility of these methods in computational mechanics.