# Theory of Continuous Media (MFGE509) Course Detail

Course Name Course Code Season Lecture Hours Application Hours Lab Hours Credit ECTS
Theory of Continuous Media MFGE509 Elective Courses 3 0 0 3 5
Pre-requisite Course(s)
N/A
Course Language English Elective Courses Natural & Applied Sciences Master's Degree Face To Face Lecture, Question and Answer, Drill and Practice. Asst. Prof. Dr. Besim Baranoğlu 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. Introduction, vector and tensor algebra and integral identities; stress vector and stress components, principal stresses and directions, rate-of-deformation tensor, spin tensor, Eulerian and Lagrangian formulations, rotation and stretch tensors, compatibility conditions, conservation of mass, linear momentum, angular momentum, first law of thermody

### 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 2
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 Kütlenin korunumu. 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 Final exam period All Chapters
16 Final exam period All Chapters

### 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 An ability to apply advanced knowledge in computational and/or manufacturing technologies to solve manufacturing engineering problems . X
2 An ability to define and analyze issues related with manufacturing technologies. X
3 An ability to develop a solution based approach and a model for an engineering problem and design and manage an experiment. X
4 An ability to design a comprehensive manufacturing system based on creative utilization of fundamental engineering principles while fulfilling sustainability in environment and manufacturability and economic constraints. X
5 An ability to chose and use modern technologies and engineering tools for manufacturing engineering applications. X
6 Ability to perform scientific research and/or carry out innovative projects that are within the scope of manufacturing engineering. X
7 An ability to utilize information technologies efficiently to acquire datum and analyze critically, articulate the outcome and make decision accordingly. X
8 An ability to attain self-confidence and necessary organizational work skills to participate in multi-diciplinary and interdiciplinary teams as well as act individually. X
9 An ability to attain efficient communication skills in Turkish and English both verbally and orally. X
10 An ability to reach knowledge and to attain life-long learning and self-improvement skills, to follow recent advances in science and technology. X
11 An awareness and responsibility about professional, legal, ethical and social issues in manufacturing engineering. X
12 An awareness about solution focused project and risk management, enterpreneurship, innovative and sustainable development. X
13 An understanding on the effects of engineering applications on health, social and legal aspects at universal and local level during decision making process. X

Activities Number Duration (Hours) Total Workload
Course Hours (Including Exam Week: 16 x Total Hours)
Laboratory
Application
Special Course Internship
Field Work
Study Hours Out of Class 16 2 32
Presentation/Seminar Prepration
Project
Report
Homework Assignments
Quizzes/Studio Critics
Prepration of Midterm Exams/Midterm Jury
Prepration of Final Exams/Final Jury 1 14 14