Dimensionless scaling of the penalty parameter for DEM–FEM volume coupling

Hybrid DEM–FEM methods with overlapping domains offer accurate yet affordable modeling of dense granular systems. A key practical question is how to choose the coupling penalty parameter, which enforces displacement compatibility without polluting the overlap solution. We propose a compact, discretization-agnostic scaling law that expresses penalty parameter as a dimensionless constant times the ratio of the effective modulus to the product of a characteristic particle size and the hybrid-zone thickness. When confinement effects are relevant, a multiplicative correction based on the effective Poisson’s ratio and lateral-stress ratio can be included, though this has negligible impact for the results reported here. Verification on a one-dimensional monodisperse column and a confined polydisperse compaction demonstrates that the proposed scaling unifies penalty choices across varying mesh sizes and overlap thicknesses, and that a dimensionless constant of approximately 10 drives the mean-stress deviation to approximately 0% for the monodisperse cases and within 2.4% for the polydisperse case, reaching a saturation plateau beyond which further increases in penalty parameter bring no accuracy benefit. The rule provides a simple, portable recipe for selecting penalty parameter in DEM–FEM volume coupling.