科目名 Course Title
Solid Mechanics and Materials（固体力学 E） [Solid Mechanics and Materials]
講義題目 Subtitle
責任教員 Instructor
佐々木 克彦 [Katsuhiko SASAKI] (大学院工学研究院)
担当教員 Other Instructors
加藤 博之(大学院工学研究院)
開講年度 Year
2013
時間割番号 Course Number
092365
開講学期 Semester
２学期
単位数 Number of Credits
2
補足事項 Other Information
キーワード Key Words
Material Strength, Elastic Deformation, Plastic Deformation, Stress, Strain, Yield Surface, Constitutive Model
授業の目標 Course Objectives
It is very important for the design of mechanical products to choose the most suitable material. The deformation of materials is roughly divided into
two regions i.e., elasticity and plasticity, and these deformations lead to fractures of materials. Therefore, the deformation mechanism of the
elasticity and plasticity should be well understood from both macroscopic and microscopic point of view. This course aims to understand some
basic theories for the elastic and plastic deformation, which are based on the historical continuum theory, and also to understand the fracture
mechanism from the microscopic point of view.
到達目標 Course Goals
Understanding some basic theories for the elastic and plastic deformation, which are based on the historical continuum theory, and also how to
apply the knowledge to real problems.
授業計画 Course Schedule
1. Basics of linear elasticity 1: tensor descriptions of stress, strain, and Hooke's law
2. Basics of linear elasticity 2: Hooke's law, the equilibrium in stress components, compatibility in strain
3. Conservative equations in elasticity: the equation of continuity, the strain energy function
4. Method of Airy's stress function: plane stress problem, complex stress function
5. Variational principle of elasticity
6. Approximation method of boundary value problem 1: fundamentals of finite element method
7. Approximation method of boundary value problem 2: fundamentals of finite element method
8. Approximation method of boundary value problem 3: Boundary element method
9. Outline of plastic deformation: true stress, true strain, incompressibility, Bauschinger effect
10. Iinitial yield stress, yield function, von Mises's yield criterion, Tresca's yield criterion, equivalent stress
11. Subsequent yield surface, isotropic hardening rule, kinematic hardening rule, combined hardening rule
12. Constitutive modelling for plasticity (1): stress invariant, deviatoric stress, incremental strain theory
13. Constitutive modelling for plasticity (2): theory of plastic potential, plastic flow, associate flow rule
14. Constitutive equation for creep deformation
15. Introduction of damage mechanics for next step
準備学習（予習・復習）等の内容と分量 Homework
Preparation: 1 hour
Brush up: 2 hours
成績評価の基準と方法 Grading System
20%: class participation
30%: Assignments (4-5 assignments are required during the term)
50%: Final exam
テキスト・教科書 Textbooks
Handout made by the course instructor will be delivered
講義指定図書 Reading List
参照ホームページ Websites
研究室のホームページ Website of Laboratory
備考 Additional Information
Finite Element Method: O.C. Zienkiewicz, R.L. Taylor, and J.Z. Zhu, Elsevier.
Engineering plasticity -theory and application to metal forming processes-: R. A. C. Slater, Macmillan.
Mathematical theory of elasticity: I.S.Sokolnikoff, 2nd, McGraw-Hill Book Co., 1956.