Boundary conditions for a dual particle method

We present a meshfree particle method suitable for computation of the dynamic response of materials. The method employs two sets of Lagrange particles: one carrying position and velocity (motion particles) and the other carrying field (stress particles). A stability analysis shows the method to be stable, even under deformation and when the connectivity is changing. This provides hope that large deformations can be computed in a Lagrange frame. Important aspects of the method include: (1) linear moving least squares (MLS) derivative estimates, (2) a unified boundary treatment based on constrained linear MLS fits, (3) a conceptually simple neighbor search that handles large anisotropy in the particle spacing, and most importantly, (4) stability with deformation and changing connectivity.