Solving adhesive rough contact problems with Atomic Force Microscope data

TL;DR

This work advances adhesive rough contact modeling by embedding AFM-derived surface topography and spatially varying adhesion properties into the MPJR interface finite element framework, using a Lennard–Jones–type traction law with regularization calibrated by AFM data. The method maps the AFM height field $z_{ij}$ and local adhesion metrics into interface integration points, enabling 2D/3D simulations that capture the interplay between roughness, adhesion, and bulk heterogeneity. Applications to a PS–LDPE sample show that fully heterogeneous bulk properties and spatially varying adhesion fields critically influence contact responses and detachment loads, with homogenized bulk predictions overestimating peak loads by about 20%. The approach bridges experimental AFM measurements with high-fidelity simulations and has broad potential for nanoscale tribology, wear studies, and multi-field fracture–adhesion problems, with future work including nonlinear and frictional effects.

Abstract

This study presents an advanced numerical framework that integrates experimentally acquired Atomic Force Microscope (AFM) data into high-fidelity simulations for adhesive rough contact problems, bridging the gap between experimental physics and computational mechanics. The proposed approach extends the eMbedded Profile for Joint Roughness (MPJR) interface finite element method to incorporate both surface topography and spatially varying adhesion properties, imported directly from AFM measurements. The adhesion behavior is modeled using a modified Lennard-Jones potential, which is locally parameterized based on the AFM-extracted adhesion peak force and energy dissipation data. The effectiveness of this method is demonstrated through 2D and 3D finite element simulations of a heterogeneous PS-LDPE (polystyrene matrix with low-density polyethylene inclusions) sample, where the bulk elastic properties are also experimentally characterized via AFM. The results highlight the significance of accounting for both surface adhesion variability and material bulk heterogeneity in accurately predicting contact responses.

Figures (24)

• Figure 1: AFM schemes: (a) force-time plot of the scanning; (b) force-distance curve with main variables.
• Figure 2: Solid domains $\Omega_{i=1,2}$ coming into contact at the nominally smooth interface $\Gamma^*$.
• Figure 3: Nominally smooth interface $\Gamma^*$ with embedded rough surface defined by the roughness function $h(\boldsymbol{\xi})$, and its discretization in MPJR interface finite elements.
• Figure 4: 2D and 3D interface finite elements.
• Figure 5: Lennard-Jones potential employed as the interface constitutive law.