Finger deformation tensor time derivative

The upper-convected time derivative is a time derivative in a special coordinate system whose base coordinate vectors stretch and rotate with material lines. With this definition of the upper-convected time derivative, stresses are produced only when material elements are deformed mere rotation produces no stress (see Section 1.4). Because of the way it is defined, the upper-convected time (teriva-tive of the Finger tensor is identically zero (see eqs. 2.2.3S and 1.4.13) ... 

One major discrepancy of the previous model can be attributed to the use of the infinitesimal strain tensor and to derivatives restricted to time changes. Indeed, in the case of large deformations, one has to refer to finite strain tensors, such as the Finger (, t (t ) or Cauchy C t(t ) strain tensors (t being the... 

To see the consequences implied by this equation of state, it is instructive to consider first simple shear flow conditions. We may write down the time dependent Finger tensor immediately, just by replacing in Eq. (7.98), derived for a deformed rubber, 7 by the increment t) — 7(t ) This results in... 

---

See also in sourсe #XX -- [ ]

---