elasticity tensor is a fourth-rank tensor describing the stress-strain relation in a linear elastic material. Other names are elastic modulus tensor and...

mechanics (stress, elasticity, quantum mechanics, fluid mechanics, moment of inertia, ...), electrodynamics (electromagnetic tensor, Maxwell tensor, permittivity...

is used is the infinitesimal strain tensor; the resulting (predicted) material behavior is termed linear elasticity, which (for isotropic media) is called...

deformation tensors. In 1839, George Green introduced a deformation tensor known as the right Cauchy–Green deformation tensor or Green's deformation tensor (the...

the first and second Piola–Kirchhoff stress tensors, the Biot stress tensor, and the Kirchhoff stress tensor. Bending Compressive strength Critical plane...

moments) and the produced deflection are the coupling stiffnesses. The elasticity tensor is a generalization that describes all possible stretch and shear...

Cauchy stress tensor (symbol ⁠ σ {\displaystyle {\boldsymbol {\sigma }}} ⁠, named after Augustin-Louis Cauchy), also called true stress tensor or simply stress...

{1}}}} be the second order identity tensor. Then the derivative of this tensor with respect to a second order tensor A {\displaystyle {\boldsymbol {A}}}...

{\sigma }}} is the Cauchy stress tensor, ε {\displaystyle {\boldsymbol {\varepsilon }}} is the infinitesimal strain tensor, u {\displaystyle \mathbf {u}...

of Elasticity, Dover, ISBN 0-486-67865-2 P.C. Chou, N. J. Pagano, Elasticity: Tensor, Dyadic, and Engineering Approaches, Dover, ISBN 0-486-66958-0 R.W...

An elastic modulus (also known as modulus of elasticity (MOE)) is a quantity that describes an object's or substance's resistance to being deformed elastically...

is a fourth-order tensor (that is, a linear map between second-order tensors) usually called the stiffness tensor or elasticity tensor. One may also write...

ISO 80000-4 (Mechanics), as a "tensor quantity representing the deformation of matter caused by stress. Strain tensor is symmetric and has three linear...

tensors used in finite strain theory, e.g. the Lagrangian finite strain tensor E {\displaystyle \mathbf {E} } , and the Eulerian finite strain tensor...

of tensor theory. For expositions of tensor theory from different points of view, see: Tensor Tensor (intrinsic definition) Application of tensor theory...

notation and manipulation for tensors and tensor fields on a differentiable manifold, with or without a metric tensor or connection. It is also the modern...

rate tensor, C {\textstyle \mathbf {C} } is the fourth-order tensor representing the constant of proportionality, called the viscosity or elasticity tensor...

Curvilinear Coordinates Wikiversity:Introduction to Elasticity/Tensors#The divergence of a tensor field – Wikiversity, Introduction to Elasticity/Tensors....

ceases to be true for tensors of rank 6 and higher), so the number of independent constants in the (fourth-rank) elasticity tensor are reduced to 5 (from...

a Cartesian tensor uses an orthonormal basis to represent a tensor in a Euclidean space in the form of components. Converting a tensor's components from...

differential geometry, the torsion tensor is a tensor that is associated to any affine connection. The torsion tensor is a bilinear map of two input vectors...

rate tensor, C {\textstyle \mathbf {C} } is the fourth-order tensor representing the constant of proportionality, called the viscosity or elasticity tensor...

infinitesimal strain and L i j k l {\displaystyle L_{ijkl}} is the elasticity tensor, a fourth-rank tensor with 81 components (usually 21 independent components)...

is the stress tensor, ε the strain tensor, I the identity matrix and tr the trace function. Hooke's law may be written in terms of tensor components using...

_{0}\left({\partial ^{2} \over \partial \Omega ^{2}}u\right)_{\Omega =\Omega _{0}}} Elasticity tensor Volumetric strain "Bulk Elastic Properties". hyperphysics. Georgia...

\nu } . Any two of these parameters are sufficient to fully describe elasticity in an isotropic material. For example, calculating physical properties...

learning, the term tensor informally refers to two different concepts (i) a way of organizing data and (ii) a multilinear (tensor) transformation. Data...

characteristic directions; such as the principal directions of its elasticity tensor. Uni-directional ply's for example always have their first axis aligned...

single component of a tensor. Clockwork Elasto-capillarity Rubber elasticity Landau, L.D.; Lifshitz, E. M. (1986). Theory of Elasticity (3rd ed.). Oxford...

= lim t → ∞ G ( t ) {\displaystyle G=\lim _{t\to \infty }G(t)} . Elasticity tensor Dynamic modulus Impulse excitation technique Shear strength Seismic...