A Novel Approach to Multiscale MD/FE Simulations of Frictional Contacts

Abstract

In most applications, frictional contacts lead to a noticeable amount of wear, which influences the further frictional behavior. Thus, friction and wear have to be analyzed as a whole to gain powerful models. In such models the interactions of macroscopic and microscopic aspects have to be taken into account. Finite element (FE) simulations are the standard method to simulate macroscopic solid body mechanics. However, they are not suitable to represent microscopic behavior of bodies, especially abrasive friction depending on the roughness of the contact. In these applications, molecular dynamics (MD) simulations using explicit time integration schemes are a much better tool. The combination of both methods is an established approach for the solution of friction problems, which has been pursued by several authors. The usual way of linking both methods is to use MD domains for the boundary of contacting bodies modeled in FE instead of conventional contact elements. The interface between FE and MD domain is generally implemented by defining MD particles and FE nodes as coincident. With this approach, every time step of the MD simulation requires solving a linear equation system for the whole FE modeled solid. The computational cost of solving a sparse linear equation system is superlinearly dependent on its degrees of freedom. Furthermore, MD simulations use explicit time integration, which requires very small time steps to assure stability. Thus, it is disadvantageous to apply the current coupling method to large geometries, since large linear equation systems would have to be solved very often. In consequence, a different approach is required to apply multiscale MD/FE methods to complex geometries.

This paper introduces a novel approach to integrate multiscale capabilities into FE that allows solving large models at reasonable computational cost. The proposed approach integrates MD coupling into FE contact elements characterized by a nonlinear, history dependent friction law, which is trained with MD simulations. The roughness profile of sliding surfaces is modeled with elasto-plastic spherical caps serving as a mesoscopic level. The Hertzian contact between two spherical caps is handled at the microscopic level using an improved variant of the conventional node particle coincidence technique.