Vol. 16, No. 4, 2021

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

Volume 19
Issue 4, 541–572
Issue 3, 303–540
Issue 2, 157–302
Issue 1, 1–156

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 5 issues

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
Ethics and policies
Peer-review process
Submission guidelines
Submission form
Editorial board
ISSN (electronic): 1559-3959
ISSN (print): 1559-3959
Author index
To appear
Other MSP journals
This article is available for purchase or by subscription. See below.
The closest isotropic, cubic and transversely isotropic stiffness and compliance tensor to an arbitrary anisotropic material

Xinyuan Shao, Peter D. Folkow and Morteza Eskandari-Ghadi

Vol. 16 (2021), No. 4, 451–470

The aim of this paper is to provide, in the framework of Green elasticity, the closest or nearest fourth-order isotropic, cubic and transversely isotropic elasticity tensors with higher symmetries for a general anisotropic elasticity tensor or any other tensors with lower symmetry. Using a gauge parameter, the procedure is done on a dimensionless form based on different generalized Euclidean distances, namely conventional, log-, and power-Euclidean distance functions. In the case of power-Euclidean distance functions, results are presented for powers of 0.5, 1 and 2. Except for the conventional distance function, the different generalized distance functions adopted in this paper preserve the property of invariance by inversion, meaning that the results for the closest stiffness tensor are also valid for the compliance tensor. Explicit formulations are given for determining the closest isotropic and cubic tensors, where the multiplication tables of the bases are diagonal. More involved coupled equations are given for the coefficients of the closest transversely isotropic elasticity tensors, which can be solved numerically. Two different material cases are studied in the numerical examples, which illustrate the material coefficients and error measures based on the present methods, including the influence from the gauge parameter.

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:

conventional distance, log-distance, power-Euclidean distance, closest elasticity tensor, linear vector space
Received: 14 August 2020
Revised: 7 May 2021
Accepted: 1 June 2021
Published: 9 November 2021
Xinyuan Shao
Applied Mechanics Masters Program
Chalmers University of Technology
41296 Gothenburg
Peter D. Folkow
Department of Mechanics and Maritime Sciences
Chalmers University of Technology
41296 Gothenburg
Morteza Eskandari-Ghadi
School of Civil Engineering
University of Tehran
Tehran 1417466191