Particular elastic constants
Authier, A. and
Zarembowitch, A.,
International Tables for Crystallography
(2013).
Vol. D,
Section 1.3.3.4,
p.
[ doi:10.1107/97809553602060000902 ]
1.3.3.4.3. Young's modulus, Poisson's ratio
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If the applied stress reduces to a uniaxial stress,, the strain tensor is of the form In particular, We deduce from this that Young's modulus (equation
1.3.3.1 ...
Definition
Authier, A. and
Zarembowitch, A.,
International Tables for Crystallography
(2013).
Vol. D,
Section 1.3.3.2.1,
p.
[ doi:10.1107/97809553602060000902 ]
in Section 1.1.3.4
. Let us take the contracted product of the two sides of each of the two equations of (
1.3.3.2) by the components and of any two vectors, x and y : The left-hand sides are bilinear forms since ...
Elastic constants
Authier, A. and
Zarembowitch, A.,
International Tables for Crystallography
(2013).
Vol. D,
Section 1.3.3.2,
p.
[ doi:10.1107/97809553602060000902 ]
(). Poisson's ratio,, defined in Section
1.3.3.4.3, is then equal to 0.25, taking into account the relations between and given in Section
1.3.3.2.3 . In practice, Table
1.3.3.2 shows that in real crystals is never equal to 0.25 ...
Young's modulus, Poisson's ratio
Authier, A. and
Zarembowitch, A.,
International Tables for Crystallography
(2013).
Vol. D,
Section 1.3.3.4.3,
p.
[ doi:10.1107/97809553602060000902 ]
properties
If the applied stress reduces to a uniaxial stress,, the strain tensor is of the form In particular, We deduce from this that Young's modulus (equation
1.3.3.1) is
The elongation of a bar under ...
Linear elasticity
Authier, A. and
Zarembowitch, A.,
International Tables for Crystallography
(2013).
Vol. D,
Section 1.3.3,
p.
[ doi:10.1107/97809553602060000902 ]
(). Poisson's ratio,, defined in Section
1.3.3.4.3, is then equal to 0.25, taking into account the relations between and given in Section
1.3.3.2.3 . In practice, Table
1.3.3.2 shows that in real crystals is never equal to 0.25 ...
Linear compressibility
Authier, A. and
Zarembowitch, A.,
International Tables for Crystallography
(2013).
Vol. D,
Section 1.3.3.4.2,
p.
[ doi:10.1107/97809553602060000902 ]
...
Isotropic materials
Authier, A. and
Zarembowitch, A.,
International Tables for Crystallography
(2013).
Vol. D,
Section 1.3.3.5,
p.
[ doi:10.1107/97809553602060000902 ]
properties
The isotropy relation between elastic compliances and elastic stiffnesses is given in Section
1.3.3.2.3 . For reasons of symmetry, the directions of the eigenvectors of the stress and strain tensors are necessarily ...
Elastic strain energy
Authier, A. and
Zarembowitch, A.,
International Tables for Crystallography
(2013).
Vol. D,
Section 1.3.3.3,
p.
[ doi:10.1107/97809553602060000902 ]
(
1.3.3.2), one gets for the density of strain energy
References
International Tables for Crystallography (2013). Vol. D. ch. 1.3, pp. 82-83
© International Union of Crystallography 2013 ...
Variation of Young's modulus with orientation
Authier, A. and
Zarembowitch, A.,
International Tables for Crystallography
(2013).
Vol. D,
Section 1.3.3.4.4,
p.
[ doi:10.1107/97809553602060000902 ]
1.1.4.10.4
and
1.3.3.2.3).
The representation surface of, the inverse of Young's modulus, is illustrated in Figure
1.3.3.4 for crystals of different symmetries. As predicted by the Neumann principle ...
Equilibrium conditions of elasticity for isotropic media
Authier, A. and
Zarembowitch, A.,
International Tables for Crystallography
(2013).
Vol. D,
Section 1.3.3.6,
p.
[ doi:10.1107/97809553602060000902 ]
: Recalling that the condition becomes a condition on the displacement vector, : In an isotropic orthonormal medium, this equation, projected on the axis, can be written with the aid of relations (
1.3.3.5) and (
1.3.3.9 ...
