熱壓成型錐形體（cone）的簡易黏彈性行為相關問題已在過去研究 [J PolEng, 32, 245 (2012)] 經由共旋Maxwell 方程式Co-rotational Maxwell model（CM）導出了以時間為函數的薄膜變形數值解，並同時發現了未求出解的非線性常微分方程所對應的上部流Maxwell 方程式Upper Convected Maxwell Model（UCM）。本研究使用有限差分法繼續探討UCM方程式，並透過加入薄膜初始曲率來延伸探討薄膜下垂度（sag）。研究中將熱壓成型製程分作兩個階段首先為自由成型，接著為拘束成型（熔膠碰觸到錐形模具開始），研究中發現薄膜在成型前的曲率對於最後求出的熱壓成型時間會有影響，反之若初始薄膜為平坦時影響較小，而在拘束成型部分發現UCM 方程對模具錐體角度對整體成型時間影響較CM方程中小，並將此結果經由無因次處理，建立時間和曲率的關係圖。

Our previous work [J Pol Eng, 32, 245 (2012)] explores the role of viscoelasticity for the simplest relevant problem in thermoforming, the manufacture of cones. In this previous work, we use a differential model employing the corotational derivative [the corotational Maxwell model (CM)] for which we find an analytical solution for the sheet deformation as a function of time. This previous work also identifies the ordinary
nonlinear differential equation corresponding to the upper convected Maxwell model (UCM), for which she finds no analytical solution. In this paper, we explore the role of the convected derivative by solving this UCM equation numerically by finite difference. We extend the previous work to include sag by incorporating a finite initial sheet curvature. We treat both steps in thermoforming: first free forming followed by constrained (where the melt touches the conical mold). We find that the convected derivative makes the forming times (for free forming) unreasonably sensitive to the initial curvature. Whereas, for the CM model, we get a free forming time that is independent of initial sheet curvature, so long as the sheet is nearly flat to begin with. For constrained forming, we find that the CM model is sensitive to the cone angle within the conical mold, whereas, for the UCM model, we get a constrained forming time that is nearly independent of the cone angle. We cast our results into dimensionless plots of thermoforming times versus disk radius of curvature.