Novozhilov's mean rotation measures invariance

Tardin, Rodrigo H.; Santiago, J.A.F.; Cezário, Felippe de Oliveira

doi:10.1590/s1678-58782005000300013

Cited by 1 publication

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References 2 publications

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“…As an alternative measure of mean rotation, Novozhilov [37] proposed to evaluate the spatial mean of the tangent of Cauchy's mean rotation angle, as opposed to the mean of the angle itself, over all initially co-planar material vectors. Invariant formulations of this idea appeared later in Truesdell & Toupin [47] and de Oliviera et al [38]. While simpler to evaluate, Novozhilov's version of the mean rotation angle suffers from singularities due to the use of the tangent function (de Oliviera et al [38]).…”

Section: Dynamically Consistent Mean Rotation Anglesmentioning

confidence: 99%

“…Invariant formulations of this idea appeared later in Truesdell & Toupin [47] and de Oliviera et al [38]. While simpler to evaluate, Novozhilov's version of the mean rotation angle suffers from singularities due to the use of the tangent function (de Oliviera et al [38]). Finally, Marzano [31] proposed the mean of the cosine of Cauchy's angle as a measure of mean rotation.…”

Section: Dynamically Consistent Mean Rotation Anglesmentioning

confidence: 99%

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Dynamic rotation and stretch tensors from a dynamic polar decomposition

Haller

2016

Journal of the Mechanics and Physics of Solids

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The local rigid-body component of continuum deformation is typically characterized by the rotation tensor, obtained from the polar decomposition of the deformation gradient. Beyond its well-known merits, the polar rotation tensor also has a lesser known dynamical inconsistency: it does not satisfy the fundamental superposition principle of rigid-body rotations over adjacent time intervals. As a consequence, the polar rotation diverts from the observed mean material rotation of fibers in fluids, and introduces a purely kinematic memory effect into computed material rotation. Here we derive a generalized polar decomposition for linear processes that yields a unique, dynamically consistent rotation component, the dynamic rotation tensor, for the deformation gradient. The left dynamic stretch tensor is objective, and shares the principal strain values and axes with its classic polar counterpart. Unlike its classic polar counterpart, however, the dynamic stretch tensor evolves in time without spin. The dynamic rotation tensor further decomposes into a spatially constant mean rotation tensor and a dynamically consistent relative rotation tensor that is objective for planar deformations. We also obtain simple expressions for dynamic analogues of Cauchy's mean rotation angle that characterize a deforming body objectively. *

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Section: Dynamically Consistent Mean Rotation Anglesmentioning

confidence: 99%