Subject Group of Mechanical and Intelligent System Engineering
27202
Solid Mechanics and Materials
Winter
Description and rationale: 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.
Keywords:
method
elasticity, plasticity, tensor, continuum mechanics, finite element method, boundary element
Pre-requisite: none
Expected students: master and doctoral
Instructors:
Dr Hiroyuki KATO (hkato@eng.hokudai.ac.jp)
Dr Katsuhiko SASAKI (katsu@eng.hokudai.ac.jp)
Course outline:
The course is divided into two parts (2 sections); elasticity and plasticity. The responsible instructor of each
section is Dr. Kato for elasticity (1-8) and Dr. Sasaki for plasticity (9-15).
Part
1.
2.
3.
4.
5.
6.
7.
8.
1: Elasticity
Basics of linear elasticity 1: tensor descriptions of stress, strain, and Hooke's law
Basics of linear elasticity 2: Hooke's law, the equilibrium in stress components, compatibility in strain
Conservative equations in elasticity: the equation of continuity, the strain energy function
Method of Airy's stress function: plane stress problem, complex stress function
Variational principle of elasticity
Approximation method of boundary value problem 1: fundamentals of finite element method
Approximation method of boundary value problem 2: fundamentals of finite element method
Approximation method of boundary value problem 3: Boundary element method
Part 2: Plasticity
9. Outline of plastic deformation: true stress, true strain, incompressibility, Bauschinger effect
10. Yield criterion (1): initial yield stress, yield function, von Mises’s yield criterion
11. Yield criterion (2): Tresca’s yield criterion, plane, equivalent stress
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
Grading:
20%: class participation
30%: Assignments (4-5 assignments are required during the term)
50%: Final exam
Textbooks and references:
1) Handout made by the course instructor will be delivered.
2) References are shown below.
*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.
*available at the library
7/2008