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Volume 116
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Dimensionless scaling of the penalty parameter for DEM–FEM volume coupling (Open Access)
Akhil Mathews a *, Hongyang Cheng b, Miguel Angel Celigueta c, Jin Y. Ooi a
a School of Engineering, Institute for Infrastructure and Environment, The University of Edinburgh, The King's Buildings, Edinburgh, EH9 3JL, United Kingdom
b Department of Civil Engineering & Management, Faculty of Engineering Technology, University of Twente, P.O. Box 217, Enschede, 7500 AE, the Netherlands
c Altair EDEM, Spain
10.1016/j.partic.2026.06.017
Volume 116, September 2026, Pages 119-125
Received 13 September 2025, Revised 9 June 2026, Accepted 16 June 2026, Available online 24 June 2026, Version of Record 29 June 2026.
E-mail: amathews@ed.ac.uk
Highlights

• A compact scaling law sets the penalty parameter for DEM-FEM displacement continuity.

• Scaling verified across meshes, particle diameter, overlap sizes, and particle stiffness.

• At a dimensionless constant of ~10, mean stress matches ground truth DEM.

• Provides simple, portable rule for robust DEM–FEM hybrid coupling.


Abstract

Hybrid DEM–FEM methods with overlapping domains offer accurate yet affordable modelling 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, discretisation-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.

Graphical abstract
Keywords
DEM–FEM coupling; Penalty method; Hybrid overlap; Scaling law; Granular mechanics
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