UCC/UGC/ECCC
Proposal for New Course
Please attach proposed Syllabus in approved university format.
1. Course subject and number: ME 561
2. Units:
See upper and lower division undergraduate course definitions.
3. College:
CEFNS
4. Academic Unit:
3
Mechanical Engineering
5. Student Learning Outcomes of the new course. (Resources & Examples for Developing Course Learning
Outcomes)








Describe the stress-strain curve observed experimentally for metals (LO 1,2,5)
Use physical models to describe plastic behavior of materials in 1D (LO 1,5)
Use index notion to perform mathematical calculations (LO 1,5,11)
Define stress and strain as tensors at a point in 2D and 3D (LO 1,5)
Define, visualize, and apply yield and failure criteria (LO 1,5)
Define and apply conditions of equilibrium and compatibility (LO 1,5)
Define and apply elastic stress-strain relations (LO 1,5)
Explain the difference between elastic and plastic behavior of materials and how that difference
is expressed mathematically (LO 1,5,11).
 Explain the key features of the theory plasticity including: yield function, hardening rules, flow
rule, consistency condition, and loading index (LO 1,5,11)
 Explain why the yield surface must be convex, i.e. explain Drucker’s postulate (LO 1,5,11)
 Explain how plasticity theory is solved numerically and can be integrated into finite element
codes (LO 1,5,11)
Note: LO refers to mechanical engineering learning outcomes (which can be found at
https://nau.edu/CEFNS/Engineering/Mechanical/Degrees-Programs/).
6. Justification for new course, including how the course contributes to degree program outcomes,
or other university requirements / student learning outcomes. (Resources, Examples & Tools for Developing
Effective Program Student Learning Outcomes).
This course will expand our graduate course offerings to give our M.Eng., M.S., and Ph.D. students
more choices in classes. Furthermore, a course in plasticity is offered at the masters or doctoral level
in civil and/or mechanical engineering at most universities. To fit the needs of NAU students, this
course offers more background information and more of an applied approach compared to graduate
level courses in plasticity at other universities. Finally, as can be seen from the learning outcomes,
this course is related to ABET criteria (a) An ability to apply knowledge of mathematics, science, and
engineering, (e) An ability to identify, formulate, and solve engineering problems, and (k) An ability
to use the techniques, skills, and modern engineering tools necessary for engineering practice.
Effective Fall 2012
7. Effective BEGINNING of what term and year?
Fall 2015
See effective dates calendar.
8. Long course title: ENGINEERING PLASTICITY
(max 100 characters including spaces)
9. Short course title: ENGINEERING PLASTICITY
(max. 30 characters including spaces)
10. Catalog course description (max. 60 words, excluding requisites):
This course is a practical approach to modeling the plastic behavior of materials. Topics
include: physical models, index notion, elastic stress-strain relations, yield and failure
criteria, perfectly plastic models, work hardening models, and integration of models into
finite element software. Prerequisites: ME 365 (Machine Design) or CENE 376 (Structural
Analysis I), and MAT 239 (Differential Equations) with grade greater than or equal to C.
11. Will this course be part of any plan (major, minor or certificate) or sub plan (emphasis)?
Yes
No
If yes, include the appropriate plan proposal.
Mechanical Engineering; M.S.E. / MENG Elective. No related plan changes are needed.
12. Does this course duplicate content of existing courses?
Yes
No
If yes, list the courses with duplicate material. If the duplication is greater than 20%, explain why
NAU should establish this course.
13. Will this course impact any other academic unit’s enrollment or plan(s)?
Yes
No
If yes, describe the impact. If applicable, include evidence of notification to and/or response from
each impacted academic unit
14. Grading option:
Letter grade
Pass/Fail
Both
15. Co-convened with:
14a. UGC approval date*:
(For example: ESE 450 and ESE 550) See co-convening policy.
*Must be approved by UGC before UCC submission, and both course syllabi must be presented.
16. Cross-listed with:
(For example: ES 450 and DIS 450) See cross listing policy.
Please submit a single cross-listed syllabus that will be used for all cross-listed courses.
17. May course be repeated for additional units?
16a. If yes, maximum units allowed?
16b. If yes, may course be repeated for additional units in the same term?
18. Prerequisites:
Effective Fall 2012
ME 365 (Machine Design) or
Yes
No
Yes
No
CENE 376 (Structural Analysis I),
and MAT 239 (Differential
Equations) with grade greater
than or equal to C.
If prerequisites, include the rationale for the prerequisites.
Topics from these courses will directly used in ME 561. In particular the stress/strain analysis from
ME 365 or CENE 376 will be used and plasticity theory is built on a system of differential equations,
so students must have knowledge from MAT 239. These classes are typically completed by the
senior year in both civil and mechanical engineering
19. Co requisites:
If co requisites, include the rationale for the co requisites.
20. Does this course include combined lecture and lab components?
Yes
If yes, include the units specific to each component in the course description above.
21. Names of the current faculty qualified to teach this course:
No
Heidi Feigenbaum
22. Classes scheduled before the regular term begins and/or after the regular term ends may require
additional action. Review “see description” and “see impacts” for “Classes Starting/Ending
Outside Regular Term” under the heading “Forms”
http://nau.edu/Registrar/Faculty-Resources/Schedule-of-Classes-Maintenance/.
Do you anticipate this course will be scheduled outside the regular term?
Yes
No
23. Is this course being proposed for Liberal Studies designation?
If yes, include a Liberal Studies proposal and syllabus with this proposal.
Yes
No
24. Is this course being proposed for Diversity designation?
If yes, include a Diversity proposal and syllabus with this proposal.
Yes
No
Answer 22-23 for UCC/ECCC only:
FLAGSTAFF MOUNTAIN CAMPUS
Scott Galland
Reviewed by Curriculum Process Associate
10/23/2014
Date
Approvals:
F. Ernesto Penado
Department Chair/Unit Head (if appropriate)
10/20/2014
Date
Chair of college curriculum committee
Date
Effective Fall 2012
Dean of college
Date
For Committee use only:
UCC/UGC Approval
Date
Approved as submitted:
Yes
No
Approved as modified:
Yes
No
EXTENDED CAMPUSES
Reviewed by Curriculum Process Associate
Date
Approvals:
Academic Unit Head
Date
Division Curriculum Committee (Yuma, Yavapai, or Personalized Learning)
Date
Division Administrator in Extended Campuses (Yuma, Yavapai, or Personalized
Learning)
Date
Faculty Chair of Extended Campuses Curriculum Committee (Yuma, Yavapai, or
Personalized Learning)
Date
Chief Academic Officer; Extended Campuses (or Designee)
Date
Approved as submitted:
Yes
No
Approved as modified:
Yes
No
Effective Fall 2012
Plasticity
Spring Semester 2013
NAU College of Engineering, Forestry and Natural Science
Mechanical Engineering Department
Instructor:
Heidi Feigenbaum
Office: Room 201
Phone: 523-5326
E-mail: hf38@nau.edu
Office Hours: Mon. 1-3pm, Tues & Thurs 1-2pm, and by appointment
Class Schedule:
T/Th 11:10-12:25 PM, Engineering Rm. 218
Prerequisites:
ME 365 (Machine Design) or CENE 376 (Structural Analysis I), and MAT 239 (Differential Equations)
with grades of C or better.
If you have not completed the prerequisites for a course as stated in the
academic catalog, you may be administratively dropped from the course before the twenty-first day of
the term. Do not rely on your instructor to drop you from the courses that you want to drop. You are
responsible for changing your own course schedule.
Course Description:
This course is a practical approach to modeling the plastic behavior of materials. Topics include:
physical models, index notion, elastic stress-strain relations, yield and failure criteria, perfectly plastic
models, work hardening models, and integration of models into finite element software. 3hrs.
Lecture.
Learning Outcomes:
Upon completion of this class, students will be able to:
 Describe the stress-strain curve observed experimentally for metals (LO 1,2,5)
 Use physical models to describe plastic behavior of materials in 1D (LO 1,5)
 Use index notion to perform mathematical calculations (LO 1,5,11)
 Define stress and strain as tensors at a point in 2D and 3D (LO 1,5)
 Define, visualize, and apply yield and failure criteria (LO 1,5)
 Define and apply conditions of equilibrium and compatibility (LO 1,5)
 Define and apply elastic stress-strain relations (LO 1,5)
 Explain the difference between elastic and plastic behavior of materials and how that
difference is expressed mathematically (LO 1,5,11).
 Explain the key features of the theory plasticity including: yield function, hardening rules,
flow rule, consistency condition, and loading index (LO 1,5,11)
 Explain why the yield surface must be convex, i.e. explain Drucker’s postulate (LO 1,5,11)
 Explain how plasticity theory is solved numerically and can be integrated into finite element
codes (LO 1,5,11)
Effective Fall 2012
Note: LO refers to mechanical engineering learning outcomes (which can be found at
https://nau.edu/CEFNS/Engineering/Mechanical/Degrees-Programs/).
Course Structure:
For the most part, this is a traditional lecture-style class, however, I encourage questions from the
class. During class, we will solve problems as a class or in small groups. Everyone MUST
participate in solving these problems.
Required Text:
Plasticity for Structural Engineers, Wai-Fah Chen and Da-Jian Han, J. Ross Publishing, 2007.
References:
Introduction to Engineering Plasticity, G.K. Lal and N. Venkata Teddy, Alpha Science, 2009
Theory of Plasticity, J. Chakrabarty, 3rd edition, Elsevier Butterworth-Heinemann, 2006.
Advanced Strength and Applied Elasticity, 5th Edition, Ansel C. Ugural and Saul K. Fenster, Pearson,
2012
Advanced Mechanics of Materials, 2nd edition, R. D. Cook, Prentice Hall, 1999
In addition, any calculus, mechanics of materials and elasticity textbooks are good references for this
class.
Grading System:
RELATIVE WEIGHT
Homework
Midterm Exam 1
Midterm Exam 2
Project
Total
25%
25%
25%
25%
100%
As typical, 90-100% semester average will be an A, 80-90% semester average will be a B, 70-80%
semester average will be a C, 60-70% semester average will be a D and less than 60% semester
average will be a F.
Exam grades may be scaled, but only if necessary and still subject to an absolute standard. Under
no circumstances will homework or project grades be scaled.
Course Policies:
1. Office Hours: Please honor the scheduled office hours, and make an appointment for alternate
times. Not during scheduled office hours, if my door is open, I might be available to answer
questions, however, if my door is closed, please respect that I am busy and come back at another
time or email me to schedule an appointment.
2. Reading Assignments: I will not explicitly assign reading from the textbook. You are responsible
keeping up to date with where we are in the textbook and reading along. Reading prepares you
for and reinforces the lecture. Any outside reading assignments or handouts will be posted on
BBLearn.
Effective Fall 2012
3. Attendance: Regular attendance is expected (see policy in NAU general catalog:
http://www4.nau.edu/academiccatalog/2010/Introduction/Important_Policies/Combined/ClassAtten
d.htm). When absence is unavoidable, students assume the responsibility for any work they miss.
Instructors are under no obligation to make special arrangements for students who have been
absent unless the student has an institutional excuse.
4. Attitude and Conduct: You are expected to reflect the same professionalism that is expected of
practicing engineers. At a minimum this means that you must be respectful to your classmates
and me. No texting, sleeping, Internet searching, chitchatting, etc. during class. I will ask you to
leave if you are not being respectful to me and/or other students. See
http://home.nau.edu/studentlife/handbook/appendix_f.asp for NAU’s Classroom Management
statement.
5. Academic Integrity: As defined in the Student Handbook (for additional information consult the
handbook’s web page at http://home.nau.edu/studentlife/handbook.asp, Appendix G, Academic
Dishonesty), academic integrity means that students and faculty jointly agree to adhere to a code
of conduct appropriate to the mutually trusting relationship that must exist between student and
teacher. Those values will not allow either to take credit for work not their own, or to be deceitful
in any way, or to take unfair advantage of other students or of each other, or to be other than
totally truthful and straightforward in all that they do. In particular, keep in mind that exceptionally
high standards of honor and integrity are fundamental and essential to the study and practice of
engineering. See Engineering Students' Professional and Code of Conduct Policy document from
the college for more information.
6. Academic Dishonesty: Academic dishonesty is a form of misconduct that is subject to disciplinary
action under the Student Code of Conduct. It will not be tolerated in this class and could result in
failing the course or even expulsion from the college and university. If you are charged with
academic dishonesty, you are subject to the Arizona Board of Regents’ Code of Conduct and
procedures established by NAU that are outlined in the NAU Student Handbook. Academic
dishonesty includes plagiarism, cheating, fabrication, fraud, and facilitating academic dishonesty.
The possible consequences of academic dishonesty vary from a reduced or zero grade on the
assignment or examination to a failing grade in the course. In extreme cases, suspension and/or
dismissal from the university may be penalties, especially for students with past records of
academic dishonesty. See the NAU Student Handbook, Appendix G, for more information and
additional examples. Keep in mind that engineering is considered to be an ethical profession, and
engineering students are expected to display the highest ethical standards. Furthermore, not
knowing that certain activities qualify as academic dishonesty is not a defense to a charge of
academic dishonesty.
Cheating: is the intentional use of, or attempted use of, unauthorized materials, information, study
aids, or previously prepared solutions in any academic exercise, exam, paper or other assignment.
For example, a student who communicates with other students during an exam (either directly or
through bits of paper, hand signals or electronic devices) or who uses materials that are not allowed
in the exam. Another example is given by students who get up from their seats (to ask questions
from the instructor or to go to the restroom) and cheat by glancing at other students’ papers.
Conversely, a student may get up but leaves his/her exam uncovered, allowing other students to
easily see their work (see also plagiarism below).
Collusion: occurs when two or more students work together to produce individually submitted work
without the permission of the faculty member. Collusion also occurs when one student produces work
Effective Fall 2012
and knowingly allows another student to copy it and submit that copy for assessment. In such a
case, both students will be considered to have colluded. Similarly, any student who helps another
student to commit any type of academic dishonesty is considered to have colluded. Note that in
engineering assignments it is OK to work in groups in order to discuss the solution to a problem, but
the actual calculations performed to obtain the solution should be individually done.
Fabrication/Fraud: is the unauthorized falsification or invention of any information, data, or citation
in an academic exercise. It also includes any attempt to deceive a faculty member or administrative
officer of the university regarding academic work. For example, a student who falsely uses illness or
other form of extenuating circumstance to obtain an extension on an exam or assignment. As
another example, consider a student whose final answer to a homework problem does not match the
answer in the back of the book, but the student writes the answer in the book on his/her paper
anyway. This is a fraudulent situation that can be easily detected, since it will be obvious that the
calculations are inconsistent with the answer (and in some cases the answer in the book may be
wrong). A similar situation occurs when a student presents a solution to a problem with insufficient
calculations to justify the answer, and this answer magically matches the answer in the book or the
answer obtained by other students in the class.
Obtaining an unfair advantage: includes activities that directly or indirectly compromise fair
assessment or grading or constrain other students’ abilities to successfully complete their
assignments. As examples, consider gaining access to examination materials prior to the time
authorized by the faculty member, or destroying reference materials with the result that others are
deprived of their use, or circulating previously administered examinations (unless authorized by the
faculty member).
Plagiarism: representing the words, expressions, productions or creative works of another as one’s
own in any academic exercise. For example, consider a student who simply copies the solution to a
problem from others or from a solutions manual or from the solution to a similar problem assigned in
a previous semester. Another example is given by a student who submits a computer assignment
that is simply a copy (or effectively a copy) of another student’s work. An additional example is given
by a student who either completely or partially copies a report or assignment from another student or
even from the web.
7. Homework: It is impossible for you to do well in this course without doing the homework.
a. Homework is part of your grade and is due at the beginning of the lecture period on the due
date. Late homework will not be accepted. Exceptions to the late homework policy are
allowable only under the NAU student excused policy guidelines (illness, official athletic
activities, etc.) and written authorization from the appropriate medical or NAU authority is
mandatory. If you have an institutional excuse, arrangements must be made with the
instructor prior to the date when you will be absent. Remember also that you can always
turn in an assignment early or electronically.
b. In order to accommodate different circumstances, the lowest homework grade will be
dropped at the end of the semester.
c. High standards of workmanship are expected by the profession owing to the great
responsibility attached to the practice of engineering, and similarly will be required for all
homework assignments. Please pay particular attention to turning in a professional-looking
assignment (neat, orderly, etc.).
8. Exams: Two midterms exams will be given during the semester.
a. Make-up exams: Only under the most extreme circumstances will a make-up exam be
given (e.g. illness or an institutional excuse). In all cases for a make-up exam to be given
Effective Fall 2012
written authorization from the appropriate medical or NAU authority is mandatory. Such
missed events must be rescheduled within one week of the subject absence, or prior to the
final exam, whichever is sooner, and must be scheduled at least 48 hours in advance.
Permission to take a make-up exam must be obtained prior to missing the exam. Only if
there is an emergency will you be allowed to make up an exam that you missed without
discussing your situation with me before the exam and again you must have written
authorization.
b. Re-grades: If you are unhappy with your grade on a midterm exam, you may submit the
exam for re-grading. Please include with your exam a short memo explaining where you
feel points were unfairly deducted. When you submit your exam for re-grading, the whole
test will be re-graded and there is no guarantee that your grade will be better than what you
had before. Re-grades must be submitted within one week of when the exam is returned to
the class.
University Policies:
You can find additional important NAU academic policies at the links below. Please take a few
minutes to review and become familiar with them.
See http://www4.nau.edu/avpaa/UCCPolicy/plcystmt.html for policies on:
 Safe Environment Policy
 Students With Disabilities
 Institutional Review Board
 Academic Integrity
 Academic Contact Hour Policy
 Sensitive Course Materials
See http://home.nau.edu/studentlife/handbook/appendix_f.asp for
 Classroom Management statement.
You can find information about drop/add deadlines at the following link for the Office of the Registrar’s
enrollment calendar website: http://nau.edu/Registrar/Important-Dates/Fall-Enrollment-Calendar2012/
Effective Fall 2012
TENTATIVE SCHEDULE**
Day
Tu
Th
Tu
Th
Tu
Th
Tu
Th
Tu
Th
Tu
Th
Tu
Th
Tu
Th
Tu
Th
Tu
Th
Tu
Th
Tu
Th
Tu
Th
Tu
Th
Tu
Th
DATE
15-Jan
17-Jan
22-Jan
24-Jan
29-Jan
31-Jan
5-Feb
7-Feb
12-Feb
14-Feb
19-Feb
21-Feb
26-Feb
28-Feb
5-Mar
7-Mar
12-Mar
14-Mar
26-Mar
28-Mar
2-Apr
4-Apr
9-Apr
11-Apr
16-Apr
18-Apr
23-Apr
25-Apr
30-Apr
2-May
Topic
Introduction
Experimental Stress-Strain Curves & Mechanisms of plastic deformation
Physical models for plastic behavior
Index Notation
Stress & Equilibrium
Yield and Failure Criteria
Strain & Deformation
Elastic stress-strain relations
Flow rule
Review & Catch up
MIDTERM EXAM 1 - Tenative
Example
Incremental stress-strain relations
Convexity
Hardening
Loading index and consistency condition
Incremental stress-strain relations
Example: Isotropic hardening
Project proposal discussions
Example: Prager's kinematic hardening
Example: Armstrong-Frederick kinematic hardening
Example: Mixed hardening
FE implimenation
FE implimenation
Numerical Algorithms for solving nonlinear equations
Numerical Implementation
Review & Catch up
MIDTERM EXAM 2 - Tenative
Project Presentations
Project Presentations
Chapters
1.3
1.4
1.5
2.1
2.2-2.4
3.1
3.2-3.3
4.1-4.3
4.7
4.8
4.6
5.1
5.2-5.3
5.7
5.6
5.6
5.6
5.6
6.1-6.3
6.1-6.3
6.4
6.5
** This course outline is tentative and is likely to change over the course of the semester. I will not
post updated schedules. It is your responsibility to stay up to date with the course including what
we are covering in lecture and the topics to be covered on each exam.
Effective Fall 2012