Sentence examples for rotation gradient from inspiring English sources

The averaged control volume rotation 〈ω〉c is calculated by a linear interpolation of the beam-midpoint rotations to be consistent with the constant rotation gradient.

Because the couple stresses μ are proportional to the rotation gradient ∇ω, the continuum and beam systems match badly near the specimen corners where both micro-rotations and micro-rotation gradients are high and rapidly alternating.

In analogy, by taking moments of the compatibility equations, micromechanical expressions are obtained for the (infinitesimal) kinematic quantities average rotation gradient tensor and average Cosserat strain tensor in the two-dimensional case.

In analogy, the expressions for the average rotation gradient tensor and the average Cosserat strain tensor are obtained from considerations of the change of length and change of rotation of a line element in the two-dimensional case.

Twins and matrix were significantly distorted relative to each other (by about 3° on average) and showed a strong rotation gradient from top to bottom, revealing that the whole grain is bent.

From Eq. (14) it follows that the non-zero components of the couple stress μ have the same indices as the non-zero entries of the rotation gradient ∇ω: begin{array}{*{20}l} langle boldsymbol{mu}rangle_{mathrm{c}} &= langle{mu_{zx}}rangle_{mathrm{c}} boldsymbol{e}_{z} otimes boldsymbol{e}_{x} + langle{mu_{zy}}rangle_{mathrm{c}} boldsymbol{e}_{z} otimes boldsymbol{e}_{y}, end{array} (24).

This leads to the local rotation (buckling) of columnar chains within shear bands at failure, being associated with a softening behavior, development of large voids, generation of high particle rotation gradients, rapid decrease of internal energy and rapid increase of dissipated energy within the shear bands at macro scale.

This semi-analytical, energy based ansatz is used to obtain, from local stresses and deformations in the discrete model, continuous fields for a micropolar description of the deformation state in terms of displacement gradients, micro- and macro-rotations, and micro-rotation gradients, and of the stress state in terms of the corresponding conjugate stress variables.

With these restrictions, the liquid velocity becomes a superposition of the solid-body rotation and the gradient of a velocity potential.

Another caution regarding the usage is the effect of rotation or the gradient of the fingertip while the participants tried to maintain the posture of their finger during the exploration in our experiments.

As a consequence of the centrifugal force, ρ νθ2/r, induced by the rotation, a pressure gradient is formed in the cylindrical containing tube, with low pressure along the axis.