On the strain energy distribution of two elastic solids under smooth contact

The Hertz contact law for two linear elastic spheres plays a very important role in the discrete element method (DEM). Within the classic Hertz contact theory, the contact strain energy distribution in the two contacting spheres is analytically derived, which states that the ratio between the strain energies stored in the two spheres is solely dependent on their material properties, regardless of their radii. This strain distribution law is generally valid for non-spherical and other contact cases, provided that the two surfaces in contact can be reasonably treated as two elastic half-spaces and that the deformation is small. The independence feature of the law from the contact geometry also greatly facilitates the computation of the contact strain energy stored at particle level. As a direct consequence of this law, the contact point between two particles in DEM could also be determined. The numerical simulations demonstrate good agreement between the theoretical prediction and the numerical results for the tested cases involving spheres and ellipsoids with varying sizes and material properties. (c) 2021 Elsevier B.V. All rights reserved.

Automated summary

The Hertz contact law is crucial in DEM for analyzing contact strain energy distribution in two linear elastic spheres. The independence feature of this law simplifies computation of contact strain energy at particle level.