Quasistatic adhesive contact of visco-elastic bodies and its numerical treatment for very small viscosity

TL;DR

This paper investigates the quasistatic adhesive contact of visco-elastic bodies with very small viscosity, analyzing the asymptotic behavior as viscosity approaches zero and demonstrating numerical simulations using boundary-element methods.

Contribution

It introduces a novel asymptotic analysis for small viscosity in visco-elastic adhesive contact and develops a numerical scheme for simulation.

Findings

As viscosity approaches zero, a defect-like measure captures additional energy dissipation.

Numerical simulations validate the asymptotic analysis and demonstrate the method's effectiveness.

The boundary-element method effectively models the quasistatic adhesive contact with small viscosity.

Abstract

An adhesive unilateral contact of elastic bodies with a small viscosity in the linear Kelvin-Voigt rheology at small strains is scrutinized. The flow-rule for debonding the adhesive is considered rate-independent and unidirectional, and inertia is neglected. The asymptotics for the viscosity approaching zero towards purely elastic material involves a certain defect-like measure recording in some sense natural additional energy dissipated in the bulk due to (vanishing) viscosity, which is demonstrated on particular 2-dimensional computational simulations based on a semi-implicit time discretisation and a spacial discretisation implemented by boundary-element method.