we will review the discoveries in the field of nonlinear theology of entangled polymers since 2006 when it was first reported that synthetic polymers could undergo inhomogeneous shear beyond the stress overshoot during startup shear and show non-quiescent relaxation after a large step strain [1-2] In the past decade, we have attempted to develop a realistic understanding to address the following two central questions in polymer theology: (a) how chain deformation takes place, (b) when and why affine deformation ceases [3,41 The emerging phenomenology, initially derived from the application of particle-tracking velocimetric (PTV) method, has greatly helped us to revise the existing experimental and theoretical paradigms. The observed strain localization phenomena in both continuous shear [5] and extension l61 are clearly the sources of various polymer processing instabilities in the manufacturing ofpolymer products at an annual rate ofhundred million tons.
