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A level set method for simulating wrinkling of extruded viscoelastic sheets
Polymer Engineering and Science ( IF 3.2 ) Pub Date : 2020-06-15 , DOI: 10.1002/pen.25409 Kalonji K. Kabanemi 1 , Jean‐Philippe Marcotte 1
Polymer Engineering and Science ( IF 3.2 ) Pub Date : 2020-06-15 , DOI: 10.1002/pen.25409 Kalonji K. Kabanemi 1 , Jean‐Philippe Marcotte 1
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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, σc, for the onset of wrinkling of an elastic sheet scales like σc~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 (σc being small), in accordance with numerical predictions.
中文翻译：
模拟挤出粘弹性片材起皱的水平设定方法
当聚合物从横截面纵横比大的矩形模具中自由挤出时，会观察到皱纹。这种皱纹虽然在挤压的牛顿材料中不存在，但会在挤压的粘弹性片中形成，并被认为是由弹性应力驱动的不稳定性。本研究致力于开发一种瞬态有限元方法，该方法将基于矩阵对数的构象张量公式和单相水平集方法相结合，用于模拟在粘弹性流体的片材挤出过程中形成的皱纹。板料挤压的数值分析是在较大的流量范围和模具出口横截面的宽厚比χ下进行的，以确定挤出片材起皱的关键条件。对于大的纵横比，即，χ >> 1，皱纹开发在温和的挤出流量，对应于基于瑞利能源方法表现出大约29计算一个魏森伯格数，临界压缩应力，σ Ç，对于发病起皱的弹性片鳞等的σ c ^〜1 / χ 2，具有用于显著下降χ >> 1。作为毗邻模头出口唇，压缩正常应力在挤出片材引起的，起皱将发生于大χ（σ Ç 较小），根据数值预测。
更新日期：2020-06-15
中文翻译：
模拟挤出粘弹性片材起皱的水平设定方法
当聚合物从横截面纵横比大的矩形模具中自由挤出时，会观察到皱纹。这种皱纹虽然在挤压的牛顿材料中不存在，但会在挤压的粘弹性片中形成，并被认为是由弹性应力驱动的不稳定性。本研究致力于开发一种瞬态有限元方法，该方法将基于矩阵对数的构象张量公式和单相水平集方法相结合，用于模拟在粘弹性流体的片材挤出过程中形成的皱纹。板料挤压的数值分析是在较大的流量范围和模具出口横截面的宽厚比χ下进行的，以确定挤出片材起皱的关键条件。对于大的纵横比，即，χ >> 1，皱纹开发在温和的挤出流量，对应于基于瑞利能源方法表现出大约29计算一个魏森伯格数，临界压缩应力，σ Ç，对于发病起皱的弹性片鳞等的σ c ^〜1 / χ 2，具有用于显著下降χ >> 1。作为毗邻模头出口唇，压缩正常应力在挤出片材引起的，起皱将发生于大χ（σ Ç 较小），根据数值预测。
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