# 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 3 0 0 3 5
Pre-requisite Course(s)
Consent of the instructor
Course Language English N/A Natural & Applied Sciences Master's Degree 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

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 expand and get in-depth information with scientific researches in the field of mechanical engineering, evaluate information, review and implement.
2 Have comprehensive knowledge about current techniques and methods and their limitations in Mechanical engineering.
3 To complete and apply knowledge by using scientific methods using uncertain, limited or incomplete data; use information from different disciplines.
4 Being aware of the new and developing practices of Mechanical Engineering and being able to examine and learn when needed.
5 Ability to define and formulate problems related to Mechanical Engineering and develop methods for solving and apply innovative methods in solutions.
6 Ability to develop new and/or original ideas and methods; design complex systems or processes and develop innovative/alternative solutions in the designs.
7 Ability to design and apply theoretical, experimental and modeling based researches; analyze and solve complex problems encountered in this process.
8 Work effectively in disciplinary and multi-disciplinary teams, lead leadership in such teams and develop solution approaches in complex situations; work independently and take responsibility.
9 To establish oral and written communication by using a foreign language at least at the level of European Language Portfolio B2 General Level.
10 Ability to convey the process and results of their studies systematically and clearly in written and oral form in national and international environments.
11 To know the social, environmental, health, security, law dimensions, project management and business life applications of engineering applications and to be aware of the constraints of their engineering applications.
12 Ability to observe social, scientific and ethical values in the stages of data collection, interpretation and announcement and in all professional activities.

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