Strain and stress tensors
Authier, A. and
Zarembowitch, A.,
International Tables for Crystallography
(2013).
Vol. D,
Section 1.3.6.3,
p.
[ doi:10.1107/97809553602060000902 ]
is
In a material description, the strain components are defined by the following equations: Substituting (
1.3.6.6) into (
1.3.6.7), it follows that Hence
If the products and squares of the displacement derivatives are neglected ...
Second-order and higher-order elastic stiffnesses
Authier, A. and
Zarembowitch, A.,
International Tables for Crystallography
(2013).
Vol. D,
Section 1.3.6.4,
p.
[ doi:10.1107/97809553602060000902 ]
coefficients. Table
1.3.6.2 gives the values of the third-order stiffnesses of some materials.
Table
1.3.6.1 | top | pdf |
Number of independent third-order elastic stiffnesses for each Laue class ...
Nonlinear elasticity
Authier, A. and
Zarembowitch, A.,
International Tables for Crystallography
(2013).
Vol. D,
Section 1.3.6,
p.
[ doi:10.1107/97809553602060000902 ]
The converse of (
1.3.6.1) and (
1.3.6.2) may be written where
A spatial description or Eulerian description uses the independent variables (t,,,), the being called spatial coordinates.
Now, for the sake ...
Elastic strain-energy density
Authier, A. and
Zarembowitch, A.,
International Tables for Crystallography
(2013).
Vol. D,
Section 1.3.6.6,
p.
[ doi:10.1107/97809553602060000902 ]
...
Introduction
Authier, A. and
Zarembowitch, A.,
International Tables for Crystallography
(2013).
Vol. D,
Section 1.3.6.1,
p.
[ doi:10.1107/97809553602060000902 ]
...
Expansion of elastic constants for small initial stress
Authier, A. and
Zarembowitch, A.,
International Tables for Crystallography
(2013).
Vol. D,
Section 1.3.6.5,
p.
[ doi:10.1107/97809553602060000902 ]
...
Lagrangian and Eulerian descriptions
Authier, A. and
Zarembowitch, A.,
International Tables for Crystallography
(2013).
Vol. D,
Section 1.3.6.2,
p.
[ doi:10.1107/97809553602060000902 ]
(t,,,) as independent variables is called a material or Lagrangian description.
The converse of (
1.3.6.1) and (
1.3.6.2) may be written where
A spatial description or Eulerian description uses the independent variables ...