A theoretical model for the contact of elastoplastic bodies

Abstract

The paper presents a theoretical model for the normal contact of a rigid sphere with an elastic-perfectly plastic half-space or an elastic-perfectly plastic sphere with a rigid wall. F ormulae describing the force-displacement relationship for static contact problems and the coef cient of restitution for dynamic impact problems are derived. The present model can be considered as a modi cation of Johnson's model by using a more detailed pressure distribution function which is based on nite element analysis (F EA) results and considering the variation in the curvature of the contact surface during the contact interaction. In order to verify the theoretical model, nite element analyses are also conducted, and results are compared with those predicted by the model for both contact force-displacement relations and restitution coef cients. G ood agreements between the model predictions and the F EA results are found.

On the solution of asymptotic impact problems with significant localised indentation

“…It is only the elastoplastic loading stage that is predicted with a non-Meyer type compliance model. This is also the case with other non-Meyer type contact models [5,9,10].…”

“…Half-space impact conditions are normally used in experiments and finite element analysis to determine the response during dynamic indentation e.g. coefficient of restitution and contact time [9,21,22] and the material properties of the target e.g. dynamic yield [4,23].…”

A semi-analytical model for oblique impacts of elastoplastic spheres

“…In other words, for a given impact angle and impact speed, the rebounding kinematics of the sphere can be determined once e n and f are known (Brach 1988(Brach , 1991. Many studies have been carried out to investigate the normal coefficient of restitution e n during elastoplastic impacts, and the rebound behaviour of elastoplastic spheres during normal impacts is well established (Johnson 1987;Thornton 1997;Thornton & Ning 1998;Kharaz et al 2001;Li et al 2000Li et al , 2002Thornton et al 2001;Wu et al 2003a). The impulse ratio can be determined by measuring the initial and rebound velocities at the sphere centre (Brach 1988(Brach , 1991Cheng et al 2002).…”

Preliminary Investigations of the Low-Velocity Impact Response of a Smart Trimorph Plate for Active Damage Mitigation

“…The approximations used in [12] could lead to an underestimation of the permanent indentation at the end of the unloading. Based on published observations of the unloading response during elastoplastic indentation [14 -16], the expressions in equation (15) are proposed here to calculate . A comparison of the unloading response predicted using equation (15) and the expressions in [12] against published experimental data [17] is shown in Figure 2, and equation (15) Model [12] Experiment [17] Present (Eqs.…”