Smooth-particle applied mechanics: Conservation of angular momentum with tensile stability and velocity averaging

Smooth-particle applied mechanics (SPAM) provides several approaches to approximate solutions of the continuum equations for both fluids and solids. Though many of the usual formulations conserve mass, (linear) momentum, and energy, the angular momentum is typically not conserved by SPAM. A second difficulty with the usual formulations is that tensile stress states often exhibit an exponentially fast high-frequency short-wavelength instability, "tensile instability." We discuss these twin defects of SPAM and illustrate them for a rotating elastic body. We formulate ways to conserve angular momentum while at the same time delaying the symptoms of tensile instability for many sound-traversal times. These ideas should prove useful in more general situations.