Within the particle methods community, standard benchmark tests are needed to demonstrate that the governing equations are solved correctly.Whereas the finite element method (FEM) has long-established basic verification standards (patch tests, convergence testing, etc.), no such standards have been universally adopted within the particle method community.
As with FEM, particle methods must continue to pass patch tests, convergence, and frame/basis indifference. Of greater contemporary value is the establishment of additional verification tests that exercise particle methods in massive-deformation problems involving complicated geometries, for which they purport to be superior to traditional finite-element methods. Two large-deformation verification problems, applicable to any constitutive model, are proposed to serve as standardized verification tests suitable to quantify accuracy, robustness, and convergence of particle methods. These new verification tests not only simultaneously confirm basis and frame indifference, but one of them also involves very large shear strains which are common in the application of the particle methods to penetration problems. One of these problems involves traction-free boundaries, which is the only boundary condition handled naturally in most particle methods. The other problem separately allows testing of boundary conditions.
Available online: Verification MMS conference article