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Results for DC.creator="A." AND DC.creator="Authier" in section 1.3.6 of 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 ...
Expansion of elastic constants for small initial stress
International Tables for Crystallography (2013). Vol. D, Section 1.3.6.5, pp. 93-94 [ doi:10.1107/97809553602060000902 ]
... to expand the elastic constants in the initial state as a power series in the strain about the natural state. To ...
Second-order and higher-order elastic stiffnesses
International Tables for Crystallography (2013). Vol. D, Section 1.3.6.4, p. 93 [ doi:10.1107/97809553602060000902 ]
... strain energy per unit volume [Phi], is assumed to be a polynomial in the strain: where , , X denotes the configuration of ... first two terms in (1.3.6.9) are zero. Note that is a stress and not an intrinsic characteristic of the material. In ... isothermal stiffnesses are, respectively, where the internal energy, U, is a function of X, and [sigma], and the Helmholtz free ...
Nonlinear elasticity
International Tables for Crystallography (2013). Vol. D, Section 1.3.6, pp. 92-95 [ doi:10.1107/97809553602060000902 ]
Nonlinear elasticity 1.3.6. Nonlinear elasticity 1.3.6.1. Introduction | | In a solid body, the relation between the stress tensor T and ... equation 1.3.3.2)where the 's are the elastic stiffnesses. For a solid under finite strain conditions, Hooke's law, valid for ... Lagrangian (material) or the Eulerian (spatial) descriptions. Let us consider a fixed rectangular Cartesian coordinate system with axes (). Any ...
Lagrangian and Eulerian descriptions
International Tables for Crystallography (2013). Vol. D, Section 1.3.6.2, p. 92 [ doi:10.1107/97809553602060000902 ]
... Lagrangian (material) or the Eulerian (spatial) descriptions. Let us consider a fixed rectangular Cartesian coordinate system with axes (). Any particular position vector r of components (, , ) denotes a point in space. A point that always moves with the material is called ...
Introduction
International Tables for Crystallography (2013). Vol. D, Section 1.3.6.1, p. 92 [ doi:10.1107/97809553602060000902 ]
Introduction 1.3.6.1. Introduction In a solid body, the relation between the stress tensor T and ... equation 1.3.3.2)where the 's are the elastic stiffnesses. For a solid under finite strain conditions, Hooke's law, valid for ...
Strain and stress tensors
International Tables for Crystallography (2013). Vol. D, Section 1.3.6.3, pp. 92-93 [ doi:10.1107/97809553602060000902 ]
... stress tensors The displacement vector from the reference position of a particle to its new position has as components The term strain refers to a change in the relative positions of the material points in a body. Let a final configuration be described in terms ...
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 ...
Expansion of elastic constants for small initial stress
International Tables for Crystallography (2013). Vol. D, Section 1.3.6.5, pp. 93-94 [ doi:10.1107/97809553602060000902 ]
... to expand the elastic constants in the initial state as a power series in the strain about the natural state. To ...
Second-order and higher-order elastic stiffnesses
International Tables for Crystallography (2013). Vol. D, Section 1.3.6.4, p. 93 [ doi:10.1107/97809553602060000902 ]
... strain energy per unit volume [Phi], is assumed to be a polynomial in the strain: where , , X denotes the configuration of ... first two terms in (1.3.6.9) are zero. Note that is a stress and not an intrinsic characteristic of the material. In ... isothermal stiffnesses are, respectively, where the internal energy, U, is a function of X, and [sigma], and the Helmholtz free ...
Nonlinear elasticity
International Tables for Crystallography (2013). Vol. D, Section 1.3.6, pp. 92-95 [ doi:10.1107/97809553602060000902 ]
Nonlinear elasticity 1.3.6. Nonlinear elasticity 1.3.6.1. Introduction | | In a solid body, the relation between the stress tensor T and ... equation 1.3.3.2)where the 's are the elastic stiffnesses. For a solid under finite strain conditions, Hooke's law, valid for ... Lagrangian (material) or the Eulerian (spatial) descriptions. Let us consider a fixed rectangular Cartesian coordinate system with axes (). Any ...
Lagrangian and Eulerian descriptions
International Tables for Crystallography (2013). Vol. D, Section 1.3.6.2, p. 92 [ doi:10.1107/97809553602060000902 ]
... Lagrangian (material) or the Eulerian (spatial) descriptions. Let us consider a fixed rectangular Cartesian coordinate system with axes (). Any particular position vector r of components (, , ) denotes a point in space. A point that always moves with the material is called ...
Introduction
International Tables for Crystallography (2013). Vol. D, Section 1.3.6.1, p. 92 [ doi:10.1107/97809553602060000902 ]
Introduction 1.3.6.1. Introduction In a solid body, the relation between the stress tensor T and ... equation 1.3.3.2)where the 's are the elastic stiffnesses. For a solid under finite strain conditions, Hooke's law, valid for ...
Strain and stress tensors
International Tables for Crystallography (2013). Vol. D, Section 1.3.6.3, pp. 92-93 [ doi:10.1107/97809553602060000902 ]
... stress tensors The displacement vector from the reference position of a particle to its new position has as components The term strain refers to a change in the relative positions of the material points in a body. Let a final configuration be described in terms ...
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