Effective thermal conduction of a Signorini-type problem in composites with rough interface

TL;DR

This paper investigates how Signorini-type interface conditions influence the asymptotic thermal conduction behavior in composite materials with rough interfaces, revealing different limit problems based on interface parameters.

Contribution

It provides a detailed analysis of the asymptotic behavior of thermal conduction in composites with rough interfaces under Signorini conditions, considering various parameter regimes.

Findings

Different limit problems depending on interface parameters

Asymptotic behavior characterized as interface oscillations diminish

Impact of Signorini conditions on thermal conduction in composites

Abstract

We analyse the effect of a Signorini-type interface condition on the asymptotic behaviour, as {\epsilon} tends to zero, of a problem posed in an open bounded cylinder of {R^N}, {N\geq 2}, divided in two connected components by an imperfect rough surface. The Signorini-type condition is expressed by means of two complementary equalities involving the jump of the solution on the interface and its conormal derivative via a parameter {\gamma}. Different limit problems are obtained according to the values of {\gamma} and the amplitude of the interface oscillations.