[Paper Review] Surface pressure and shear stress field within a frictional contact on rubber

Danh Toan Nguyen, Pierdomenico Paolino+6 more|arXiv (Cornell University)|Jan 27, 2017

Mechanical stress and fatigue analysis4 references4 citations

TL;DR

This study presents a finite element-based inversion method to determine surface pressure and shear stress distributions in rubber contacts under frictional sliding, accounting for finite strains and nonlinear elasticity. By applying measured displacement fields as boundary conditions on a modeled rubber substrate, the method accurately recovers stress fields, revealing high lateral strains at contact edges and validating the approach on both linear and twisting sliding contacts.

ABSTRACT

This paper addresses the issue of the determination of the frictional stress distribution from the inversion of the measured surface displacement field for sliding interfaces between a glass lens and a rubber (poly(dimethylsiloxane)) substrate. Experimental results show that high lateral strains are achieved at the periphery of the sliding contacts. As a consequence, an accurate inversion of the displacement field requires that finite strains and non linear response of the rubber substrate are taken into account. For that purpose, a Finite Element (FE) inversion procedure is implemented where the measured displacement field is applied as a boundary condition at the upper surface of a meshed body representing the rubber substrate. Normal pressure is also determined by the same way, if non-diverging values are assumed at the contact edge. This procedure is applied to linearly sliding contacts as well as on twisting contacts.

Motivation & Objective

• To determine the distribution of surface pressure and shear stress in rubber during frictional sliding.
• To address the challenge of accurately inverting displacement fields in rubber due to large, nonlinear deformations.
• To develop a finite element-based inversion procedure that incorporates measured surface displacements as boundary conditions.
• To validate the method on both linear sliding and twisting contacts between a glass lens and PDMS rubber.
• To ensure non-diverging pressure values at the contact edge during inversion.

Proposed method

• A finite element (FE) model is constructed to represent the rubber substrate, with the measured displacement field applied as a boundary condition on its upper surface.
• The inversion procedure uses the displacement field to compute internal stress fields, including normal pressure and shear stress, by solving the equilibrium equations under finite strain conditions.
• Nonlinear hyperelastic material behavior of poly(dimethylsiloxane) (PDMS) is explicitly modeled to capture the material's response under large deformations.
• The method assumes non-diverging pressure values at the contact edge to stabilize the inversion process.
• The approach is applied to both linear sliding and twisting contact configurations to assess robustness and accuracy.
• The inversion is validated by comparing computed stress fields with experimental observations of strain localization at contact peripheries.

Experimental results

Research questions

• RQ1 How can the surface pressure and shear stress fields be accurately reconstructed from measured displacement fields in rubber contacts?
• RQ2 What role do finite strains and nonlinear elasticity play in the stress distribution during frictional sliding?
• RQ3 Can the inversion method reliably recover stress fields when large lateral strains occur at the contact edge?
• RQ4 How does the performance of the inversion method differ between linear sliding and twisting contact geometries?
• RQ5 What constraints are necessary to ensure stable and physically meaningful pressure recovery at the contact edge?

Key findings

• The finite element inversion method successfully recovers surface pressure and shear stress fields from measured displacement data, even under large deformations.
• High lateral strains are observed at the periphery of the contact, indicating significant non-uniform deformation that must be captured by the model.
• The inclusion of finite strain and nonlinear elasticity in the FE model is essential for accurate stress field reconstruction.
• The method produces non-diverging pressure values at the contact edge when appropriate constraints are applied.
• The approach is validated on both linear sliding and twisting contacts, demonstrating its robustness across different contact kinematics.
• The results show good agreement between computed stress fields and experimental displacement measurements, confirming the method's reliability.