The closest isotropic, cubic and transversely isotropic stiffness and compliance tensor to an arbitrary anisotropic material
Artikel i vetenskaplig tidskrift, 2021

The aim of this paper is to provide, in the framework of Green elasticity, the closest or nearest fourthorder
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.

closest elasticity tensor

conventional distance

power-Euclidean distance

linear vector space



Xinyuan Shao

Chalmers, Mekanik och maritima vetenskaper, Marin teknik

Peter Folkow

Chalmers, Mekanik och maritima vetenskaper, Dynamik

Morteza Eskandari-Ghadi

University of Tehran

Journal of Mechanics of Materials and Structures

1559-3959 (ISSN)

Vol. 16 4 451-470


Teknisk mekanik



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