Coordinate-free Characterization of the Symmetry Classes of Elasticity Tensors - Erratum

Abstract

We formulate coordinate-free conditions for identifying all the symmetry classes of the elasticity tensor and prove that these conditions are both necessary and sufficient. Also, we construct a natural coordinate system of this tensor without the a priory knowledge of the symmetry axes.

Full text

ERRATUM
Coordinate-free Characterization of the Symmetry
Classes of Elasticity Tensors
Andrej Bóna &Ioan Bucataru &Michael A. Slawinski
Published online: 10 July 2007
#Springer Science + Business Media B.V. 2007
1 Journal of Elasticity Volume 87(2-3) 109-132, doi: 10.1007/s10659-007-9099-z
1. Equation (5): there should be a factor of 2 in front of c_45.
The correct text should be as follows:
CeðÞ¼
c11 c12 c13 ffiffiffi
2
pc14 ffiffiffi
2
pc15 ffiffiffi
2
pc16
c12 c22 c23 ffiffiffi
2
pc24 ffiffiffi
2
pc25 ffiffiffi
2
pc26
c13 c23 c33 ffiffiffi
2
pc34 ffiffiffi
2
pc35 ffiffiffi
2
pc36
ffiffiffi
2
pc14 ffiffiffi
2
pc24 ffiffiffi
2
pc34 2c44 2c45 2c46
ffiffiffi
2
pc15 ffiffiffi
2
pc25 ffiffiffi
2
pc35 2c45 2c55 2c56
ffiffiffi
2
pc16 ffiffiffi
2
pc26 ffiffiffi
2
pc36 2c46 2c56 2c66
2
6
6
6
6
6
6
4
3
7
7
7
7
7
7
5
ð5Þ
2. Within the paragraph before equation (34)“rotation by angle qh”should be as
follows:
“rotation by angle θηðÞ
=3”
J Elasticity (2007) 88:185–186
DOI 10.1007/s10659-007-9126-0
The online version of the original article can be found at http://dx.doi.org/10.1007/s10659-007-9099-z.
A. Bóna :M. A. Slawinski
Department of Earth Sciences, Memorial University, St. John’s NL A1B 3X5, Canada
A. Bóna
e-mail: abona@mun.ca
M. A. Slawinski
e-mail: mslawins@mun.ca
I. Bucataru (*)
Faculty of Mathematics, “Al. I. Cuza”University, Iasi 700506, Romania
e-mail: bucataru@uaic.ro

3. Equation (34): there should be a factor of 3 in the denominator of the argument of the
trigonometric functions 2qþhðÞ.
The correct text should be as follows:
σ¼bkk
γ2cos ð2θþηðÞ
=3Þγ2sin ð2θþηðÞ
=3Þsin ð2θþηðÞ
=3Þ
γ2sin ð2θþη
ðÞ
=3Þγ2cos ð2θþη
ðÞ
=3Þcos ð2θþη
ðÞ
=3Þ
sin ð2θþηðÞ
=3Þcos ð2θþηðÞ
=3Þ0
2
43
5:ð34Þ
4. Equation (35): the denominator of the expression for c_44 should be multiplied by 2.
The correct text should be as follows:
c11 ¼γ1þγ3
ðÞγ2
2γ2
1þγ1þγ4
ðÞγ2
1þ2γ2þγ3
ðÞγ2
2þ2γ2þγ4
ðÞ
22þγ2
1
ðÞ
1þγ2
2
ðÞ ;
c12 ¼γ1γ3
ðÞγ2
2γ2
1þγ1γ4
ðÞγ2
1þ2γ2γ3
ðÞγ2
2þ2γ2γ4
ðÞ
22þγ2
1
ðÞ
1þγ2
2
ðÞ ;
c13 ¼γ2γ1
ðÞγ1
2þγ2
1
;c33 ¼2γ1þγ2γ2
1
2þγ2
1
;
c14 ¼γ3γ4
ðÞγ2
21þγ2
2
ðÞ
;c44 ¼γ3þγ4γ2
2
21þγ2
2
ðÞ
;
ð35Þ
186 A. Bóna et al.