Mass-Stiffness Templates for Media Interface Treatment

Abstract eng:
Mass and stiffness templates are used for the numerical treatment of a difficult interface problem that arises in the Particle Finite Element method (PFEM). We consider two one-dimensional, semi- infinite, FEM-derived, regular lattices of two media, M1 and M2, that meet an an interface point B. The M1 media extends indefinitely from B in the -x direction, while the M2 lattice extends indefinitely from B in the +x direction. The FEM discretization uses displacements and pressure as primarily variables and can treat both incompressible and compressible media when equipped with a Finite Calculus (FIC) stiffness stabilization term. Media M1 can be a linear fluid or a linear elastic isotropic solid, and likewise for M2. (Since PFEM is based on a Lagrangian formulation, the treatment of solids and fluid is unified within certain limits..) The case where M1 and M2 coalesce is aallowed and is used to remove the interface effect. The stiffness template is uniquely determined by the condition that both displacements and pressures are exact in static analysis under uniform or linearly varying body forces; in particular under a hydrostatic pressure load. The presence or absence of the interface make no difference. The selection of the mass template is more involved and delicate. It is based on the spectral treatment of arbitrary- wavelength plane waves propagated through the lattices [1]. The spectral analysis shows that certain, very particular wavelengths related to nodal spacing cause numerical instability when at least one of the media approaches exact incompressibility. Preliminary results indicated that such instability may be overcome by adding an artificial "pressure mass" to the diagonal of the mass matrix in correspondence with pressure-acceleration degrees of freedom. This appears to be a new result.

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