  We employ a first principles, force-level approach to self-consistently
construct the anharmonic tube confinement field for entangled fluids of rigid
needles and for primitive-path (PP) level chains in two limiting situations
where chain stretching is assumed to either completely relax or remain
unrelaxed. The influence of shear and extensional deformation and polymer
orientation is determined in a nonlinear elastic limit where dissipative
relaxation processes are intentionally neglected. For needles and PP-level
chains, a Gaussian analysis of transverse polymer dynamical fluctuations
predicts that deformation-induced orientation leads to tube dilation. In
contrast, for deformed polymers in which chain stretch does not relax we find
tube compression. For all three systems, a finite maximum transverse
entanglement force localizing the polymers in effective tubes is predicted. The
conditions when this entanglement force can be overcome (a force imbalance) by
an externally applied force associated with macroscopic deformation can be
crisply defined in the nonlinear elastic limit, and the possibility of a
"microscopic absolute yielding" event destroying the tube confinement can be
analyzed. For needles and contour-relaxed PP chains, this force imbalance is
found to occur at a stress of order the equilibrium shear modulus and thus a
strain of order unity, corresponding to a mechanically fragile entanglement
tube field. However, for unrelaxed stretched chains, tube compression
stabilizes transverse polymer confinement, and there appears to be no force
imbalance. These results collectively suggest that the crossover from elastic
to irreversible viscous response requires chain retraction to initiate
disentanglement. We qualitatively discuss comparisons with existing
phenomenological models for nonlinear startup shear, step strain, and creep
rheology experiments.
