A mechanically-derived contact model for adhesive elastic-perfectly plastic particles

Abstract

A contact model able to capture the response of interacting adhesive elastic-perfectly plastic particles under a variety of loadings is presented. The contact model is valid through each of the three major contact regimes: elastic, fully-plastic, and bulk elastic---all with and without adhesion.

In the elastic through fully-plastic contact regimes the model is built upon the Method of Dimensionality Reduction which allows the problem of a 3D axisymmetric contact to be mapped to a semi-equivalent 1D problem of a rigid indenter penetrating a bed of independent Hookean springs. Plasticity is accounted for by continuously varying the 1D indenter profile subject to a constraint on the contact pressure. Unloading falls out naturally, and simply requires lifting the 1D indenter out of the springs and tracking the force. Notably, by accounting for the incompressible nature of this plastic deformation, the contact model is able to detect and evolve secondary contacts caused by outward displacement of the free surface with good precision. JKR type adhesion is recovered seamlessly by simply allowing the springs to `stick’ to the 1D indenter's surface.

To complete the contact model an additional treatment for the bulk elastic contact regime, characterized by a rapid stiffening in the force-displacement curve, is proposed. A simple formulation is presented for an additional bulk elastic force related to the particle's mean surface displacement, contact areas, particle volume, and bulk modulus. A novel criterion for triggering this force (i.e. detecting the bulk elastic regime) related to the remaining free surface area of the particle is also given. This bulk elastic force is then superimposed with the force response given by the Method of Dimensionality Reduction to achieve a contact model capable of capturing a variety of complex loadings. In this way, the methodology for treating the bulk elastic regime presented here stands independent and could be appended to any contact model.

Direct comparison of all elements of the contact model are made to finite element simulations revealing the accurate predictive capabilities of the contact model.