塑性力學
Theory of Plasticity
課號: 522 M 2710

課程內容介紹:

　具延展性之材料(ductile material)，例如金屬，在受力超過彈性極限(elastic limit)時，即會產生永久變形，亦即塑性變形(plastic deformation)，而塑性力學理論(Theory of Plasticity)即是在探討材料產生塑性變形後，其變形之狀態，包括應力與應變的分佈。在彈性(elastic)範圍之變形，材料之應變僅決定於最終之受力大小;但在塑性變形範圍，材料之變形則與受力的過程(history of the loading)有關，且須遵循材料之降伏準則(yield criterion)，因此，其變形與受力的關係屬於一種非線性的增量(incremental)模式，與線性彈性變形之模式不同。
　　塑性力學理論在結構力學之應用方面可做為結構受力之極限分析（limit analysis），而對於金屬成形(metal forming)而言，塑性力學理論則是不可或缺之分析工具。
　　本課程首先將介紹材料在塑性變形區之應力與應變增量(或應變率)的關係，以及常用之降伏準則;然後將介紹材料在承受彈、塑性變形時之力學分析，進而介紹完全塑性變形(fully plastic deformation)之力學分析。參考書籍與課程大綱如下所述。


Reference Books:
1. W.F. Chen and D.J. Han, Plasticity for Structural Engineering, Gau Lih Book Co., Ltd., 1995.
2. R. Hill, The Mathematical Theory of Plasticity, Oxford University Press, 1950.
3. A.S. Khan and S. Huang, Continuum Theory of Plasticity, John Wiley & Sons, Inc., 1995
4. J. Lubliner, Plasticity Theory, Macmillan Publishing Company, 1990.
5. J. Chakrabarty, Theory of Plasticity, 2nd ed., McGraw-Hill Book Co., 1998.


Course Contents:
1 Introduction
1.1 Mechanical Behavior of Isotropic Solids
1.2 Stress
1.3 Strain

2 Fundamentals of Plasticity
2.1 Yield Criteria
2.2 Rule of Plastic Flow
2.3 Stress-Strain Relations for Work-Hardening Materials
2.4 Anisotropic Yield Criterion

3 Elastic-Plastic Problems
3.1 Bending of a Prismatic Beam
3.2 Torsion of a Prismatic Bar
3.3 Thin-Walled Tube under Combined Loadings
3.4 Expansion of a Thick Spherical Shell
3.5 Expansion of a Thick-Walled Tube

4 Limit Analysis
4.1 Theorems of Limit Analysis
4.2 Applications of the General Theorems

5 Plane Strain Problems
5.1 Sheet-Drawing Through Tapered Dies
5.2 Indentation By a Flat Punch
5.3 Bending of a Single-Notched Bar

6 Theory of Slip-Line Field
6.1 Formulation of the Plane Strain Problems
6.2 Properties of Slip-Line Field
6.3 Construction of Slip-Line Fields and Hodographs
6.4 Mixed Boundary-Valued Problems

Grade Distribution:
1. Homework: 20%
2. Midterm Examination: 40%
3. Final Examination: 40%