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Elastic properties
International Tables for Crystallography (2013). Vol. D, ch. 1.3, pp. 72-100 [ doi:10.1107/97809553602060000902 ]
... 1.3.1.1. Introduction, the notion of strain field | | Let us consider a medium that undergoes a deformation. This means that the various points of the medium ... one another. Geometrical transformations of the medium that reduce to a translation of the medium as a whole will therefore ...
Experimental determination of third- and higher-order elastic constants
International Tables for Crystallography (2013). Vol. D, Section 1.3.7.6, pp. 97-98 [ doi:10.1107/97809553602060000902 ]
... been widely used; however, the measurement of ultrasonic velocities in a solid under hydrostatic pressure cannot lead to the whole set ... comments: `According to equation of motion, the wave front is a material plane which has unit normal k in the natural state; a wave front moves from the plane to the plane ...
[more results from section 1.3.7 in volume D]
Elastic strain-energy density
International Tables for Crystallography (2013). Vol. D, Section 1.3.6.6, pp. 94-95 [ doi:10.1107/97809553602060000902 ]
... elastic strain-energy density for an anisotropic medium (for example a medium belonging to the most symmetrical groups of cubic crystals ...
[more results from section 1.3.6 in volume D]
Pressure dependence of the elastic constants
International Tables for Crystallography (2013). Vol. D, Section 1.3.5.3, p. 91 [ doi:10.1107/97809553602060000902 ]
... to explain the stress dependence of the elastic constants of a crystal. Thus, if the strain-energy density is developed in a polynomial in terms of the strain, only the first and ... has been paid to their experimental determination since they are a unique source of significant information in many fields: (i) ...
[more results from section 1.3.5 in volume D]
Pulse-echo techniques
International Tables for Crystallography (2013). Vol. D, Section 1.3.4.6.3, pp. 88-89 [ doi:10.1107/97809553602060000902 ]
... 1.3.4.2), an electronic pulse generator excites the mechanical vibrations of a piezo-electric transducer glued to one of two plane-parallel faces of a specimen. An ultrasonic pulse whose duration is of the order of a microsecond is generated and transmitted through the specimen. After ...
[more results from section 1.3.4 in volume D]
Equilibrium conditions of elasticity for isotropic media
International Tables for Crystallography (2013). Vol. D, Section 1.3.3.6, pp. 85-86 [ doi:10.1107/97809553602060000902 ]
... of elasticity, equation (1.3.3.2), this condition can be rewritten as a condition on the components of the strain tensor: Recalling that the condition becomes a condition on the displacement vector, : In an isotropic orthonormal medium ...
[more results from section 1.3.3 in volume D]
Energy density in a deformed medium
International Tables for Crystallography (2013). Vol. D, Section 1.3.2.8, pp. 79-80 [ doi:10.1107/97809553602060000902 ]
Energy density in a deformed medium 1.3.2.8. Energy density in a deformed medium Consider a medium that is subjected to a stress field . ...
[more results from section 1.3.2 in volume D]
Simple shear
International Tables for Crystallography (2013). Vol. D, Section 1.3.1.4.3, p. 76 [ doi:10.1107/97809553602060000902 ]
Simple shear 1.3.1.4.3. Simple shear Matrix has one coefficient only, a shear (Fig. 1.3.1.5c): The matrix is not symmetrical, as it contains a component of rotation. Thus we have One can show that the deformation is a pure shear associated with a rotation around . References ...
[more results from section 1.3.1 in volume D]
Glossary
International Tables for Crystallography (2013). Vol. D, Section 1.3.8, p. 98 [ doi:10.1107/97809553602060000902 ]
Glossary 1.3.8. Glossary covariant basis vector transpose of matrix A components of the displacement vector components of the strain tensor ... Boltzmann constant U internal energy F free energy References Every, A. G. & McCurdy, A. K. (1992). Second and higher order elastic constants. ...
International Tables for Crystallography (2013). Vol. D, ch. 1.3, pp. 72-100 [ doi:10.1107/97809553602060000902 ]
... 1.3.1.1. Introduction, the notion of strain field | | Let us consider a medium that undergoes a deformation. This means that the various points of the medium ... one another. Geometrical transformations of the medium that reduce to a translation of the medium as a whole will therefore ...
Experimental determination of third- and higher-order elastic constants
International Tables for Crystallography (2013). Vol. D, Section 1.3.7.6, pp. 97-98 [ doi:10.1107/97809553602060000902 ]
... been widely used; however, the measurement of ultrasonic velocities in a solid under hydrostatic pressure cannot lead to the whole set ... comments: `According to equation of motion, the wave front is a material plane which has unit normal k in the natural state; a wave front moves from the plane to the plane ...
[more results from section 1.3.7 in volume D]
Elastic strain-energy density
International Tables for Crystallography (2013). Vol. D, Section 1.3.6.6, pp. 94-95 [ doi:10.1107/97809553602060000902 ]
... elastic strain-energy density for an anisotropic medium (for example a medium belonging to the most symmetrical groups of cubic crystals ...
[more results from section 1.3.6 in volume D]
Pressure dependence of the elastic constants
International Tables for Crystallography (2013). Vol. D, Section 1.3.5.3, p. 91 [ doi:10.1107/97809553602060000902 ]
... to explain the stress dependence of the elastic constants of a crystal. Thus, if the strain-energy density is developed in a polynomial in terms of the strain, only the first and ... has been paid to their experimental determination since they are a unique source of significant information in many fields: (i) ...
[more results from section 1.3.5 in volume D]
Pulse-echo techniques
International Tables for Crystallography (2013). Vol. D, Section 1.3.4.6.3, pp. 88-89 [ doi:10.1107/97809553602060000902 ]
... 1.3.4.2), an electronic pulse generator excites the mechanical vibrations of a piezo-electric transducer glued to one of two plane-parallel faces of a specimen. An ultrasonic pulse whose duration is of the order of a microsecond is generated and transmitted through the specimen. After ...
[more results from section 1.3.4 in volume D]
Equilibrium conditions of elasticity for isotropic media
International Tables for Crystallography (2013). Vol. D, Section 1.3.3.6, pp. 85-86 [ doi:10.1107/97809553602060000902 ]
... of elasticity, equation (1.3.3.2), this condition can be rewritten as a condition on the components of the strain tensor: Recalling that the condition becomes a condition on the displacement vector, : In an isotropic orthonormal medium ...
[more results from section 1.3.3 in volume D]
Energy density in a deformed medium
International Tables for Crystallography (2013). Vol. D, Section 1.3.2.8, pp. 79-80 [ doi:10.1107/97809553602060000902 ]
Energy density in a deformed medium 1.3.2.8. Energy density in a deformed medium Consider a medium that is subjected to a stress field . ...
[more results from section 1.3.2 in volume D]
Simple shear
International Tables for Crystallography (2013). Vol. D, Section 1.3.1.4.3, p. 76 [ doi:10.1107/97809553602060000902 ]
Simple shear 1.3.1.4.3. Simple shear Matrix has one coefficient only, a shear (Fig. 1.3.1.5c): The matrix is not symmetrical, as it contains a component of rotation. Thus we have One can show that the deformation is a pure shear associated with a rotation around . References ...
[more results from section 1.3.1 in volume D]
Glossary
International Tables for Crystallography (2013). Vol. D, Section 1.3.8, p. 98 [ doi:10.1107/97809553602060000902 ]
Glossary 1.3.8. Glossary covariant basis vector transpose of matrix A components of the displacement vector components of the strain tensor ... Boltzmann constant U internal energy F free energy References Every, A. G. & McCurdy, A. K. (1992). Second and higher order elastic constants. ...
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