The derivatives of scalars, vectors, and second-order tensors with respect to second-order tensors are of considerable use in continuum mechanics. These...

non-local continuum theory leading to integral equations) Stress (physics) Stress measures Tensor calculus Tensor derivative (continuum mechanics) Theory...

Levi-Civita connection Parallel transport Ricci calculus Tensor derivative (continuum mechanics) List of formulas in Riemannian geometry Einstein, Albert...

In continuum mechanics, the material derivative describes the time rate of change of some physical quantity (like heat or momentum) of a material element...

In continuum mechanics, the strain-rate tensor or rate-of-strain tensor is a physical quantity that describes the rate of change of the strain (i.e., the...

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

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

One-form Tensor product of modules Application of tensor theory in engineering Continuum mechanics Covariant derivative Curvature Diffusion tensor MRI Einstein...

velocity field Structure tensor – Tensor related to gradients Tensor derivative (continuum mechanics) Total derivative – Type of derivative in mathematics R....

In continuum mechanics, the Cauchy stress tensor (symbol σ {\displaystyle {\boldsymbol {\sigma }}} , named after Augustin-Louis Cauchy), also called true...

Solid mechanics (also known as mechanics of solids) is the branch of continuum mechanics that studies the behavior of solid materials, especially their...

infinitesimal strain tensor ε {\displaystyle {\boldsymbol {\varepsilon }}} , we have (see Tensor derivative (continuum mechanics)) ∇ × ε = e i j k   ε...

Skew coordinates Tensors in curvilinear coordinates Frenet–Serret formulas Covariant derivative Tensor derivative (continuum mechanics) Curvilinear perspective...

mathematics, the nonmetricity tensor in differential geometry is the covariant derivative of the metric tensor. It is therefore a tensor field of order three....

quantities and deformation of matter in fluid mechanics and continuum mechanics. Elementary vector and tensor algebra in curvilinear coordinates is used...

above. Related quantities often used in continuum mechanics are the rate of deformation tensor and the spin tensor defined, respectively, as: d = 1 2 ( l...

In continuum mechanics, a compatible deformation (or strain) tensor field in a body is that unique tensor field that is obtained when the body is subjected...

theoretical physics, the spin tensor is a quantity used to describe the rotational motion of particles in spacetime. The spin tensor has application in general...

mathematical field of differential geometry, the Riemann curvature tensor or Riemann–Christoffel tensor (after Bernhard Riemann and Elwin Bruno Christoffel) is the...

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...

of the derivative. The diagrammatic notation is useful in manipulating tensor algebra. It usually involves a few simple "identities" of tensor manipulations...

In continuum mechanics, including fluid dynamics, an upper-convected time derivative or Oldroyd derivative, named after James G. Oldroyd, is the rate...

In pure and applied mathematics, quantum mechanics and computer graphics, a tensor operator generalizes the notion of operators which are scalars and...

derivative of a tensor field with respect to a vector field would be to take the components of the tensor field and take the directional derivative of...

The partial derivative of the displacement vector with respect to the material coordinates yields the material displacement gradient tensor ∇ X u {\displaystyle...

a coordinate system, a tensor defined in this way is independent of the choice of a coordinate system. The notation of a tensor is T ( σ , … , ρ , u ,...

In multilinear algebra, a tensor contraction is an operation on a tensor that arises from the canonical pairing of a vector space and its dual. In components...

Cauchy stress tensor Chapman–Enskog theory Churchill–Bernstein equation Coandă effect Computational fluid dynamics Continuum mechanics Convection–diffusion...

In mathematics and physics, a tensor field is a function assigning a tensor to each point of a region of a mathematical space (typically a Euclidean space...

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...