- 學位論文
以應力鬆弛曲線重建蠕變曲線之黏彈數學模型建立與驗證
Establishment and Verification of Viscoelastic Mathematical Models for Reconstructing Creep Behaviors based on Stress Relaxation Behaviors
摘要
材料的機械性質一直扮演很重要的角色，我們必須要了解材料的機械性質，才能進一步去使用、製造，或者避免破壞、毀損。 材料的黏彈性行為主要分成三種:滯後(Hysteresis)、應力鬆弛(Stress Relaxation)、蠕變(Creep)，如果要得知一個材料的黏彈性質，就是在實驗中測量這三種現象，得知其中應力與應變的關係。 本研究將材料的鬆弛模量(Relaxation Modulus)參數輸入至Abaqus有限元素電腦模擬軟體進行分析，得到材料的蠕變曲線。將此曲線視為黃金標準來驗證轉換數學模型的正確性。主要使用兩種方法來轉換黏彈數學模型，第一種方法是使用線性黏彈理論不可逆的熱力學方程，利用矩陣的方式來將材料的鬆弛模量轉換成相對應的蠕辦柔量(Creep Compliance)。第二種方法是利用Laplace轉換，找出材料鬆弛模量與蠕變柔量在Laplace轉換之後的關係式，從而推導出材料的蠕變柔量。 最後將兩種轉換數學模型得到的蠕變曲線，與Abaqus有限元素電腦模擬軟體分析出來的蠕變曲線做比較，來驗證此兩種轉換數學模型的正確性。
並列摘要
The mechanical properties of materials have always played a very important role. We must understand the mechanical properties of materials in order to further use, manufacture, or avoid damage. The viscoelastic behavior of materials is mainly divided into three types: Hysteresis, Stress Relaxation, and Creep. If you want to know the viscoelastic properties of a material, you need to measure these three phenomena in experiments to know the relationship between stress and strain. In this study, the Relaxation Modulus parameters of the material were input into the Abaqus finite element computer simulation software for analysis, and the Creep Curve of the material was obtained. Consider this Creep Curve the gold standard to verify the correctness of the transformation math model. Two methods are mainly used to convert the viscoelastic mathematical model. The first method is to use the irreversible thermodynamic equation of the linear viscoelastic theory, and use the matrix method to convert the relaxation Modulus of the material into the corresponding Creep Compliance. The second method is to use Laplace transformation to find out the relationship between the material Relaxation Modulus and Creep Compliance after Laplace transformation, so as to deduce the Creep Compliance of the material. Finally, compare the Creep Curve obtained by the two conversion mathematical models with the Creep Curve analyzed by the Abaqus finite element computer simulation software to verify the correctness of the two conversion mathematical models.