## Course Title : Solid Mechanics, Adv.

Code 10G003 Master Course 1st term Thu 1st C3-Lecture Room 1 2 No Restriction Lecture Japanese H. Hirakata, T. Shimada

### Course Description

This course provides fundamental concepts of solid mechanics such as stress, strain, and constitutive laws, and methods for analyzing stress/strain fields and deformation of solids and structures on the basis of the concepts. In particular, the course lectures theories of nonlinear problems such as plasticity and creep, and their numerical solutions, or finite element methods, which are important for design and development of mechanical structures.

Grading is based on the examination, possibly with considerations of the homework reports.

### Course Goals

Students will be able to:
understand solid mechanics deeply and acquire basic knowledge to design mechanical structures.
analyze problems of plasticity and creep by finite element methods.

### Course Topics

Theme Class number of times Description
Introduction 1 Overview of solid mechanics
Stress 1 Cauchy stress tensor, Equilibrium equation, Invariants
Deformation 2 Material description and spatial description, Displacement, Deformation gradient, Lagrange-Green strain and Euler-Almansi strain, Infinitesimal strain, Material time derivative
Constitutive equation: linear elasticity 1 Linear elastic stress-strain response, Hooke’s law
Principle of virtual work and principle of minimum potential energy 1 Principle of virtual work, Principle of minimum potential energy
Finite element method for linear elasticity 3 Basis of finite element method, Finite element equilibrium equations, Elements, Numerical integration
Plasticity problems 3 Plasticity theory (uniaxial and multiaxial problems, yield criteria, flow rule, hardening rule, constitutive equations), Finite element method for elasto-plastic problems
Creep problems 2 Creep theory (uniaxial and multiaxial constitutive equations), Finite element method for creep problems
Summary 1 Discussions and reports

### Textbook

Lecture materials are distributed in the classroom.

### Textbook(supplemental)

T. Kyoya, Continuum Mechanics, Morikita (2008) (in Japanese)
Y. Tomita, “Foundation and Application of Elastoplasticity” Morikita (1995) (in Japanese)
E. Neto et al., “Computational Methods for Plasticity,” John Wiley & Sons (2008).

### Prerequisite(s)

This course requires basic knowledge of mechanics of materials and solid mechanics.