Energy density in a deformed medium
Authier, A. and
Zarembowitch, A.,
International Tables for Crystallography
(2013).
Vol. D,
Section 1.3.2.8,
p.
[ doi:10.1107/97809553602060000902 ]
of the stress field and let us evaluate the work of each component of the effort. Consider a small elementary rectangular parallelepiped of sides,, (Fig.
1.3.2.8). We shall limit our calculation to the components and, which are applied ...
Condition of continuity
Authier, A. and
Zarembowitch, A.,
International Tables for Crystallography
(2013).
Vol. D,
Section 1.3.2.3,
p.
[ doi:10.1107/97809553602060000902 ]
properties
Let us return to equation (
1.3.2.1) expressing the equilibrium condition for the resultant of the forces. By replacing by the expression (
1.3.2.4), we get, after projection on the three axes, where ...
Symmetry of the stress tensor
Authier, A. and
Zarembowitch, A.,
International Tables for Crystallography
(2013).
Vol. D,
Section 1.3.2.4,
p.
[ doi:10.1107/97809553602060000902 ]
properties
Let us now consider the equilibrium condition (
1.3.2.2) relative to the resultant moment. After projection on the three axes, and using the Cartesian expression (1.1.3.4) of the vectorial products, we obtain (including ...
Boundary conditions
Authier, A. and
Zarembowitch, A.,
International Tables for Crystallography
(2013).
Vol. D,
Section 1.3.2.6,
p.
[ doi:10.1107/97809553602060000902 ]
...
General conditions of equilibrium of a solid
Authier, A. and
Zarembowitch, A.,
International Tables for Crystallography
(2013).
Vol. D,
Section 1.3.2.1,
p.
[ doi:10.1107/97809553602060000902 ]
which will be defined in Section
1.3.2.2 .
Figure
1.3.2.1
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Definition of stress: it is the limit of R dσ when the surface element dσ tends towards zero. R and R ′ are the forces to which ...
Definition of the stress tensor
Authier, A. and
Zarembowitch, A.,
International Tables for Crystallography
(2013).
Vol. D,
Section 1.3.2.2,
p.
[ doi:10.1107/97809553602060000902 ]
Let P be a point situated inside volume V,, and three orthonormal axes, and consider a plane of arbitrary orientation that cuts the three axes at Q, R and S, respectively (Fig.
1.3.2.3). The small volume element PQRS ...
Voigt's notation, reduced form of the stress tensor
Authier, A. and
Zarembowitch, A.,
International Tables for Crystallography
(2013).
Vol. D,
Section 1.3.2.5.1,
p.
[ doi:10.1107/97809553602060000902 ]
...
Interpretation of the components of the stress tensor – special forms of the stress tensor
Authier, A. and
Zarembowitch, A.,
International Tables for Crystallography
(2013).
Vol. D,
Section 1.3.2.5.2,
p.
[ doi:10.1107/97809553602060000902 ]
properties
(i) Uniaxial stress : let us consider a solid shaped like a parallelepiped whose faces are normal to three orthonormal axes (Fig.
1.3.2.5). The terms of the main diagonal of the stress tensor ...
Stress tensor
Authier, A. and
Zarembowitch, A.,
International Tables for Crystallography
(2013).
Vol. D,
Section 1.3.2,
p.
[ doi:10.1107/97809553602060000902 ]
. Pressure is represented by a scalar, and stress by a rank-two tensor, which will be defined in Section
1.3.2.2 .
Figure
1.3.2.1
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Definition of stress: it is the limit of R dσ when the surface element ...
Local properties of the stress tensor
Authier, A. and
Zarembowitch, A.,
International Tables for Crystallography
(2013).
Vol. D,
Section 1.3.2.7,
p.
[ doi:10.1107/97809553602060000902 ]
properties
(i) Normal stress and shearing stress : let us consider a surface area element dσ within the solid, the normal n to this element and the stress that is applied to it (Fig.
1.3.2.6 ...
