# Theory of Continuous Media I (MDES678) Course Detail

Course Name Course Code Season Lecture Hours Application Hours Lab Hours Credit ECTS
Theory of Continuous Media I MDES678 Area Elective 3 0 0 3 5
Pre-requisite Course(s)
Consent of the instructor
Course Language English Elective Courses Ph.D. Face To Face Lecture. This course aims to give the students the basic principles of mechanics and the mathematical backround needed to understand these principles . The course prepares the students for more advanced courses such as elasticity, plasticity, viscoelasticity, biomechanics. The students who succeeded in this course; Students will learn the basics of tensor and vector calculus. Students will understand the concepts of stress, deformation and kinematics that are needed in theory of continuous media. Students will understand the fundamental laws of physics as applied to mechanical systems. Review of tensor analysis and integral theorems; kinematics of deformation, strain tensor, compatibility condition; material derivative, deformation rate, spin and vorticity tensor; external and internal loads, Cauchy?s principle and stress tensors; basic laws of continuum mechanics (conservation of mass, continuity equation, principle of linear an

### Weekly Subjects and Releated Preparation Studies

Week Subjects Preparation
1 Indicial notation, Matrix operations by using indicial notation, Coordinate transformation Chapter 1: Vectors and Tensors in Cartesian Coordinates
2 Vector and tensor operations. Symmetric and antisymmetric tensors. Chapter 1
3 Principle stresses and principle directions of a second order tensor. Chapter 1
4 Derivatives of tensors. Chapter 1
5 Stress (traction) vector, Cauchy stress tensor, Spherical and deviatoric parts of stress tensor. Chapter 1
6 Material time derivative, Lagrangian and Eulerian descriptions, Rate of deformation and spin tensors, Deformation gradient. Chapter 3: Deformation and Kinematics
7 Green and Cauchy deformation tensors, Strain tensor, Rate of deformation gradient, Rates of strain tensors. Chapter 3
8 Geometrical measures of strains, polar decomposition of deformation gradient tensor, rotation and stretch tensors, Volume change. Chapter 3
9 Time rate of an infinitesimal volume element, area change Chapter 3
10 Piola-Kirchhoff stress tensors (first and second kinds) Chapter 3
11 Conservation of mass Chapter 4: General principles
12 Momentum equations Chapter 4
13 Energy equation (first law of thermodynamics) Chapter 4
14 Chapter 5: Some illustrative examples Chapter 5
15 Overall review -
16 Final exam -

### Sources

Course Book 1. Malvern L. E., Introduction to Mechanics of Continuous Media, Prentice-Hall, Englewood Cliffs, New Jersey (1969) 2. Fung Y. C., A First Course in Continuum Mechanics, Prentice- Hall, Englewood Cliffs, New Jersey (1977) 3. Chung T. J., Continuum Mechanics, Prentice- Hall, Englewood Cliffs, New Jersey (1988)

### Evaluation System

Requirements Number Percentage of Grade
Attendance/Participation - -
Laboratory - -
Application - -
Field Work - -
Special Course Internship - -
Quizzes/Studio Critics - -
Homework Assignments 6 30
Presentation - -
Project - -
Report - -
Seminar - -
Midterms Exams/Midterms Jury 1 30
Final Exam/Final Jury 1 40
Toplam 8 100
 Percentage of Semester Work 60 40 100

### Course Category

Core Courses X

### The Relation Between Course Learning Competencies and Program Qualifications

# Program Qualifications / Competencies Level of Contribution
1 2 3 4 5
1 Ability to carry out advanced research activities, both individual and as a member of a team X
2 Ability to evaluate research topics and comment with scientific reasoning X
3 Ability to initiate and create new methodologies, implement them on novel research areas and topics X
4 Ability to produce experimental and/or analytical data in systematic manner, discuss and evaluate data to lead scintific conclusions X
5 Ability to apply scientific philosophy on analysis, modelling and design of engineering systems X
6 Ability to synthesis available knowledge on his/her domain to initiate, to carry, complete and present novel research at international level X
7 Contribute scientific and technological advancements on engineering domain of his/her interest area X
8 Contribute industrial and scientific advancements to improve the society through research activities X

Activities Number Duration (Hours) Total Workload
Course Hours (Including Exam Week: 16 x Total Hours) 16 4 64
Laboratory
Application
Special Course Internship
Field Work
Study Hours Out of Class 16 2 32
Presentation/Seminar Prepration
Project
Report
Homework Assignments 6 3 18
Quizzes/Studio Critics
Prepration of Midterm Exams/Midterm Jury 1 8 8
Prepration of Final Exams/Final Jury 1 10 10