A level set method for simulating wrinkling of extruded viscoelastic sheets

When a polymer is extruded freely from a rectangular die of large cross-sectional aspect ratio, wrinkles are observed. While not present in extruded Newtonian materials, such wrinkles develop in extruded viscoelastic sheets and are understood as an elastic stress-driven instability. The present study is devoted in developing a transient finite element method, which combines the matrix-logarithm-based formulation of the conformation tensor and the single-phase level set method, for simulating wrinkles that form during sheet extrusion of viscoelastic fluids. Numerical analyses of sheet extrusion were conducted over a wide range of flow rate and width-to-thickness ratio of the die exit cross section, χ, to determine critical conditions for the onset of wrinkling of extruded sheets. For large aspect ratios, that is, χ >> 1 , wrinkles develop at moderate extrusion flow rate, corresponding to a Weissenberg number of about 29. Calculations based on Rayleigh's energy method show that the critical compressive stress, σ_c, for the onset of wrinkling of an elastic sheet scales like σ_c~1/χ² , with a significant drop for χ >> 1 . As next to the die exit lip, compressive normal stresses are induced in the extruded sheet, wrinkling will take place for large χ (σ_c being small), in accordance with numerical predictions.