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Strain tensor
International Tables for Crystallography (2013). Vol. D, Section 1.3.1, pp. 72-76 [ 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 ...
Pure shear
International Tables for Crystallography (2013). Vol. D, Section 1.3.1.4.2, p. 76 [ doi:10.1107/97809553602060000902 ]
Pure shear 1.3.1.4.2. Pure shear This is a pure deformation (without rotation) consisting of the superposition of two ... the cubic dilatation is zero): The quadric of elongations is a hyperbolic cylinder. References International Tables for Crystallography (2013). Vol. ...
Simple elongation
International Tables for Crystallography (2013). Vol. D, Section 1.3.1.4.1, p. 75 [ doi:10.1107/97809553602060000902 ]
... 1.3.1.5 | | Special deformations. The state after deformation is represented by a dashed line. (a) Simple elongation; (b) pure shear; (c) simple shear. References International ...
Particular components of the deformation
International Tables for Crystallography (2013). Vol. D, Section 1.3.1.4, pp. 75-76 [ doi:10.1107/97809553602060000902 ]
... 1.3.1.5 | | Special deformations. The state after deformation is represented by a dashed line. (a) Simple elongation; (b) pure shear; (c) simple shear. 1.3.1.4.2. Pure shear | | This is a pure deformation (without rotation) consisting of the superposition of ...
Geometrical interpretation of the coefficients of the strain tensor
International Tables for Crystallography (2013). Vol. D, Section 1.3.1.3.2, p. 75 [ doi:10.1107/97809553602060000902 ]
... from the generality of the following by limiting ourselves to a planar problem and assuming that point P' to which P ... planes parallel to , and , respectively. To summarize, if one considers a small cube before deformation, it becomes after deformation an arbitrary ...
Definition of the strain tensor
International Tables for Crystallography (2013). Vol. D, Section 1.3.1.3.1, pp. 74-75 [ doi:10.1107/97809553602060000902 ]
... respect to unity, one can describe the deformation locally as a homogeneous asymptotic deformation. As was shown in Section 1.3.1.2.4, it ... can be put in the form of the product of a pure deformation corresponding to the symmetric part of , , and a pure rotation corresponding to the asymmetric part, : Matrix B ...
Arbitrary but small deformations
International Tables for Crystallography (2013). Vol. D, Section 1.3.1.3, pp. 74-75 [ doi:10.1107/97809553602060000902 ]
... respect to unity, one can describe the deformation locally as a homogeneous asymptotic deformation. As was shown in Section 1.3.1.2.4, it ... can be put in the form of the product of a pure deformation corresponding to the symmetric part of , , and a pure rotation corresponding to the asymmetric part, : Matrix B ...
Quadric of elongations
International Tables for Crystallography (2013). Vol. D, Section 1.3.1.2.5, pp. 73-74 [ doi:10.1107/97809553602060000902 ]
... the length of the vector r in the deformation. Let A and S be the antisymmetric and symmetric parts of M ... of the elongation: The geometrical study of the elongation as a function of the direction of r is facilitated by introducing the quadric associated with M: where is a constant. This quadric is called the quadric of elongations, ...
Expression of any homogeneous deformation as the product of a pure rotation and a pure deformation
International Tables for Crystallography (2013). Vol. D, Section 1.3.1.2.4, p. 73 [ doi:10.1107/97809553602060000902 ]
Expression of any homogeneous deformation as the product of a pure rotation and a pure deformation 1.3.1.2.4. Expression of any homogeneous deformation as the product of a pure rotation and a pure deformation (i) Pure rotation: ...
Cubic dilatation
International Tables for Crystallography (2013). Vol. D, Section 1.3.1.2.3, pp. 72-73 [ doi:10.1107/97809553602060000902 ]
... three vectors The parallelepiped formed by these three vectors has a volume V' given by where is the determinant associated with ... matrix B, V is the volume before deformation and represents a triple scalar product. The relative variation of the volume is ...
International Tables for Crystallography (2013). Vol. D, Section 1.3.1, pp. 72-76 [ 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 ...
Pure shear
International Tables for Crystallography (2013). Vol. D, Section 1.3.1.4.2, p. 76 [ doi:10.1107/97809553602060000902 ]
Pure shear 1.3.1.4.2. Pure shear This is a pure deformation (without rotation) consisting of the superposition of two ... the cubic dilatation is zero): The quadric of elongations is a hyperbolic cylinder. References International Tables for Crystallography (2013). Vol. ...
Simple elongation
International Tables for Crystallography (2013). Vol. D, Section 1.3.1.4.1, p. 75 [ doi:10.1107/97809553602060000902 ]
... 1.3.1.5 | | Special deformations. The state after deformation is represented by a dashed line. (a) Simple elongation; (b) pure shear; (c) simple shear. References International ...
Particular components of the deformation
International Tables for Crystallography (2013). Vol. D, Section 1.3.1.4, pp. 75-76 [ doi:10.1107/97809553602060000902 ]
... 1.3.1.5 | | Special deformations. The state after deformation is represented by a dashed line. (a) Simple elongation; (b) pure shear; (c) simple shear. 1.3.1.4.2. Pure shear | | This is a pure deformation (without rotation) consisting of the superposition of ...
Geometrical interpretation of the coefficients of the strain tensor
International Tables for Crystallography (2013). Vol. D, Section 1.3.1.3.2, p. 75 [ doi:10.1107/97809553602060000902 ]
... from the generality of the following by limiting ourselves to a planar problem and assuming that point P' to which P ... planes parallel to , and , respectively. To summarize, if one considers a small cube before deformation, it becomes after deformation an arbitrary ...
Definition of the strain tensor
International Tables for Crystallography (2013). Vol. D, Section 1.3.1.3.1, pp. 74-75 [ doi:10.1107/97809553602060000902 ]
... respect to unity, one can describe the deformation locally as a homogeneous asymptotic deformation. As was shown in Section 1.3.1.2.4, it ... can be put in the form of the product of a pure deformation corresponding to the symmetric part of , , and a pure rotation corresponding to the asymmetric part, : Matrix B ...
Arbitrary but small deformations
International Tables for Crystallography (2013). Vol. D, Section 1.3.1.3, pp. 74-75 [ doi:10.1107/97809553602060000902 ]
... respect to unity, one can describe the deformation locally as a homogeneous asymptotic deformation. As was shown in Section 1.3.1.2.4, it ... can be put in the form of the product of a pure deformation corresponding to the symmetric part of , , and a pure rotation corresponding to the asymmetric part, : Matrix B ...
Quadric of elongations
International Tables for Crystallography (2013). Vol. D, Section 1.3.1.2.5, pp. 73-74 [ doi:10.1107/97809553602060000902 ]
... the length of the vector r in the deformation. Let A and S be the antisymmetric and symmetric parts of M ... of the elongation: The geometrical study of the elongation as a function of the direction of r is facilitated by introducing the quadric associated with M: where is a constant. This quadric is called the quadric of elongations, ...
Expression of any homogeneous deformation as the product of a pure rotation and a pure deformation
International Tables for Crystallography (2013). Vol. D, Section 1.3.1.2.4, p. 73 [ doi:10.1107/97809553602060000902 ]
Expression of any homogeneous deformation as the product of a pure rotation and a pure deformation 1.3.1.2.4. Expression of any homogeneous deformation as the product of a pure rotation and a pure deformation (i) Pure rotation: ...
Cubic dilatation
International Tables for Crystallography (2013). Vol. D, Section 1.3.1.2.3, pp. 72-73 [ doi:10.1107/97809553602060000902 ]
... three vectors The parallelepiped formed by these three vectors has a volume V' given by where is the determinant associated with ... matrix B, V is the volume before deformation and represents a triple scalar product. The relative variation of the volume is ...
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