Vol. 13, No. 2, 2018

Download this article
Download this article For screen
For printing
Recent Issues

Volume 16, 1 issue Volume 16, 1 issue

Volume 15, 5 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 5 issues

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 8 issues

Volume 7, 10 issues

Volume 6, 9 issues

Volume 5, 6 issues

Volume 4, 10 issues

Volume 3, 10 issues

Volume 2, 10 issues

Volume 1, 8 issues

The Journal
About the Journal
Editorial Board
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
ISSN: 1559-3959
Author Index
To Appear
Other MSP Journals
This article is available for purchase or by subscription. See below.
Burmister's problem extended to a microstructured layer

Thanasis Zisis

Vol. 13 (2018), No. 2, 203–223

The problem of calculating the displacement and stress field in a layered elastic system loaded on its surface by a certain pressure distribution often arises in engineering analysis and design, in a number of scientific areas ranging from mechanical engineering to soil mechanics and materials science. The solution of such a problem is very important and was first introduced by Biot (1935) but later it was Burmister who presented a complete solution for the stresses and displacements in a general two layer elastic system in which the lower layer is not necessarily rigid (Burmister 1943; Burmister et al. 1944). His results found great application in the field of civil engineering but nowadays can be extended to the technology of barrier, multilayered and/or functionally coatings. Furthermore, due to the ease of manufacturing and assembly, coatings with micro- or even nano-thickness are pursued by manufacturers as hybrid materials for multifunctional devices but as manufacturing scales reduce progressively, the material microstructure itself can play an important role and size effects can be dominant upon the macroscopic mechanical response of the layer/coating. In this study we focus on the loading of a microstructural layer by a normal point load and we present the corresponding Green’s functions by extending the solutions suggested by Burmister et al. in order to introduce into the generated displacement and stress fields the effect of the microstructural characteristics of the layer. In order to incorporate the layer material microstructural characteristics we use an effective generalized continuum theory, that is the couple-stress elasticity, in which the material microstructure is introduced constitutively through a length scale. The presented results suggest deviation from those suggested by Burmister et al. in the context of classical elasticity for a layer of finite thickness as well as from those suggested by Gourgiotis and Zisis (2016) in the context of couple stress elasticity for a half-plane.

PDF Access Denied

We have not been able to recognize your IP address as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 45.00:

micromechanics, couple-stress elasticity, Green's functions, microstructured layers, coatings
Received: 31 January 2018
Revised: 13 March 2018
Accepted: 19 March 2018
Published: 27 May 2018
Thanasis Zisis
Mechanics Division
National Technical University of Athens