TABLE OF CONTENTS / Surface Tension / Tensile Instability / Monaghan's Motion Equations / Stress and Rigid-Body Rotation in Continuum Mechanics / Dynamic and Static Constitutive Relations / Example Deformations with Stress and Strain Rates / Jaumann's Rigid-Body Stress Rotation Rate / Conservation of Angular Momentum / Artificial Transport Coefficients / Residual Stress Artificial Plasticity /
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The main strengths of SPAM are simplicity, flexibility, and transparency. The main weaknesses are surface and tensile instabilities, smearing and in-terpenetration of surfaces and interfaces, together with a disquieting lack angular momentum is not conserved. In this Chapter we point out mechanisms underlying these unpleasant features of SPAM and indicate means which can be used to combat them.
The excess energy associated with surfaces ( due to the reduced number of attracting neighbors ), "surface tension", is responsible for real drops' favoring the minimum-surface spherical shape. Surface tension is totally absent in macroscopic constitutive relations, and has to be added in whenever it is desirable to reproduce physical effects due to surface tension. Capillary waves, with typical wavelengths of order one millimeter and driven by surface tension, are such an effect. The situation with smooth particles is no different. If the energy is solely a function of density the dynamics is free to choose the maximum-entropy configurations consistent with the energy.
The embedded-atom potential ,
has its energy minimum when each particle has the target density ? 0 . Figure 8.1 shows the configuration which results when 225...
