Expression of strain and rotation tensor in geodetic coordinates[J] . Xü-yan Liu,Sheng-ming Huang,Quan-qiang Liang.Acta Seismologica Sinica . 2007 (3)刘序俨;黄声明;梁全强.Expression of strain and rotation tensor in geodetic coordinates.地震学报:英文版.2007.254-264...
A strain measure must vanish for any rigid body motion, and in particular for rigid body rotation. Herein, we review some strain measures commonly adopted in nonlinear continuum mechanics. They are the right Cauchy–Green deformation tensor, the Green strain tensor, and the rate of deformation ...
f is independent of the rotation part [R] of [F], which is then equivalent to saying that f is a function of the finite strain measure [EM] = (1/2)([F]T[F] − [I]) based on change of metric or, for that matter, on any member of the family of material strain tensors. ...
Analogous invariants can be defined for the symmetric and skew-symmetric parts of the velocity gradient tensor, the strain rate tensor Sij = (Aij + Aji)/2 and the rate-of-rotation tensor Wij = (Aij − Aji)/2, respectively. The non-zero second and third invariants of these tensors are...
In particular, we have studied the orientation of the vorticity vector with respect to the three eigenvectors of the local strain rate tensor and with respect to the vortex stretching vector. Additionally, we have quantified the role of system rotation on the self-amplification terms of the ...
As a notion of strain compatible with the theory of plasticity having the plastic potential of von Mises type with the normality principle as flow rule, the strain tensor is defined by integrating the rate of deformation tensor considering the material spin with the rotation tensor. For a group...
{\sigma }=0\)for the in-plane displacement vectoruusing finite element method withν = 0.19633,34. Orientation of the principal strain axes is obtained by diagonalizing the strain tensor at every point of the AFM scan grid. This requires rotation at the angleθgiven by\(\tan (2\...
revealing the prevalence of short-range disorder in moiré heterostructures. By quantitatively mapping strain tensor fields, we uncovered two regimes of structural relaxation and disentangled the electronic contributions of constituent rotation modes. Further, we found that applied heterostrain accumulates anis...
rotation tensors, we come to the model of a hemitropic material. Here, we have an additional invariant [137] and the representation of the strain energy density of a hemitropic material reads $$\begin{aligned} {\mathcal {U}}={\mathcal {U}}\left( \mathrm {tr}\,\mathbf{C},\mathrm...
To account the local rotation in the system, we use the ω as the anti-symmetric rotation tensor as defined: 2 ωxy = − 2 ωyx = ∂ uy ∂x + ∂ ux ∂y , which ω for homogenous strain will be zero. It is worth to note that the transformation relation is ...