An asymptotic approach to the adhesion of thin stiff films

TL;DR

This paper presents an asymptotic analysis and a novel numerical method for modeling the adhesion of thin stiff films between elastic structures, focusing on first-order effects and interface stiffness.

Contribution

It introduces an original numerical approach based on Nitsche's method for stiff interface problems and provides analytical and numerical insights into bonded elastic structures.

Findings

The asymptotic analysis effectively captures first-order adhesion effects.

The numerical method demonstrates high efficiency and accuracy.

Numerical examples validate the analytical approximations.

Abstract

In this paper, the asymptotic first order analysis, both mathematical and numerical, of two structures bonded together is presented. Two cases are considered, the gluing of an elastic structure with a rigid body and the gluing of two elastic structures. The glue is supposed to be elastic and to have its stiffness of the same order than those of the elastic structures. An original numerical method is developed to solve the mechanical problem of stiff interface at order 1, based on the Nitsche's method. Several numerical examples are provided to show the efficiency of both the analytical approximation and the numerical method.