A discrete element approach to evaluate stresses due to line loading on an elastic half-space

A new approach to computing sub-surface stresses in an elastic half-space subjected to a line loading is presented. The approach is based on the discrete element method (DEM) in which the material continuum is replaced by a set of convex, rigid, interacting elements connected through visco-elastic fibers. A Hertzian pressure profile with, and without surface traction is applied to a semi-infinite domain created by gluing together discrete elements. Stresses are calculated from the inter-element joint forces that develop due to relative motion of the elements. Newton’s laws are employed to simulate the motion of each element. The stress distribution obtained from the discrete element model compares very well with that obtained from continuum elasticity models. The paper illustrates the applicability of the DEM to analysis of contacts at the microlevel and serves as a foundation to further studies in fracture and fatigue of bearing materials.