ME 444 / TME 444:
Two ideas form the core of continuum mechanics: fields and flow. A field exists everywhere and varies in time and space — stress, strain, velocity, and temperature are examples. The flow of any field is governed by its equations of motion, which allow us to understand its dynamics and make useful predictions. In this class we will apply the powerful ideas of fields and flow to materials: fluids, solids, and things in-between. To speak the language of fields and flow we will build up tools of tensor mathematics. Applications and ongoing research will be incorporated wherever possible, touching on turbulence, transport, and biomechanics, among others. The course will include
- indicial notation and tensor analysis,
- concepts of stress,
- both Eulerian and Lagrangian descriptions of deformation and strain,
- conservation of mass, momentum, energy, and
- constitutive equations to describe material response.
Basic ordinary and partial differential equations, linear algebra, undergraduate fluid mechanics (ME 225) and solid mechanics (ME 226).
- Introduction to Continuum Mechanics, Fourth Edition by W. Michael Lai, David Rubin, and Erhard Krempl; or an equivalent text.
- Div, Grad, Curl, and All That: An Informal Text on Vector Calculus by H. M. Schey.
- A Student's Guide to Vectors and Tensors by Dan Fleisch, and his video, What's a tensor?
Assignments & Grading
Students prevented from attending in person because of the covid-19 pandemic can nonetheless attend lectures remotely, submit Problem Sets via email, and take exams via Zoom (synchronously). Lectures will be recorded and posted on this page. Connection information for viewing lectures via Zoom is available from the instructor, by email.
All assignments and activities associated with this course must be performed in accordance with the University of Rochester's Academic Honesty Policy. In this course, students are allowed to collaborate on Problem Sets — provided that each collaborator takes the time to fully understand the material and write a separate copy of the assignment. On exams, use of all course resources is permitted, but collaboration with other students or outside aids, including services like Chegg.com, is prohibited. Facilitating dishonesty is dishonesty. Students must write and sign the Honor Pledge on all exams: “I affirm that I will not give or receive any unauthorized help on this exam, and that all work will be my own.”
- Problem Sets - 30%
- Roughly one assignment every two weeks (see Resources), due at 23:59 Eastern time, to be submitted via GradeScope. Late Problem Sets will not be accepted.
- Midterm - 35%
- 14:00 - 15:15, 29 March, Meliora 209 or via Zoom.
- Final exam - 35%
- Tuesday, 11 May, 16:00 - 19:00, Meliora 209
I will distribute evaluations periodically to collect feedback. I typically check email frequently but cannot guarantee immediate response at all times. Quick questions can be effectively and efficiently addressed by email, but for in-depth questions a face-to-face discussion usually works better. The problem sets are intended to be hard enough to bring you into my office! Office hours take place Tuesdays 13:00-14:00 in Hopeman 218 and in my Zoom meeting room. Send email if you need to meet at another time.
This sequence may evolve as the course progresses.
- Introduction (Ch. 1)
- Tensors (Ch. 2)
- Kinematics of a Continuum (Ch. 3)
- Stress and Integral Formations of General Principles (Ch. 4)
- The Elastic Solid (Ch. 5)
- Newtonian Viscous Fluid (Ch. 6)
- Non-Newtonian Fluids (Ch. 8)
The University is committed to protecting the health and safety of the entire community – students, faculty and staff. For this reason, it is mandatory that everyone wear a mask in University buildings and observe appropriate social distancing, including classrooms. Masks have been provided to students, faculty and staff and classrooms have been specifically assigned to allow for social distancing to support these requirements. You must wear a mask appropriately (e.g. over nose and mouth) if you are attending class in person, and you must do this for every class session and for the entire duration of each class session. If you fail to do this, you will be politely reminded of the requirement and then asked to leave if you do not comply. If you do not want to wear a mask, you may consider attending via Zoom. Students who refuse to adhere to requirement for mask wearing or social distancing the course will be in violation of the COVID-19 Community Commitment and will be referred to the Student Conduct system through a COVID-19 Concern Report. Such referrals will lead to student conduct hearings and may result in disciplinary action. Students who feel unable to wear a mask may contact the Office of Disability Resources to explore options for accommodations. Students requiring accommodations may be asked to participate in the course through synchronous or asynchronous learning as part of this accommodation.
The University of Rochester respects and welcomes students of all backgrounds and abilities. The University employs professional staff committed to assisting students with disabilities in the classroom, residence halls, libraries, and elsewhere on campus. In the event you encounter any barriers to full participation in this course due to the impact of a disability, please contact the Office of Disability Resources (email@example.com, 585-276-5075). The access coordinators in the Office of Disability Resources can meet with you to discuss the barriers you are experiencing and explain the eligibility process for establishing academic accommodations. It is a personal decision to disclose the existence of a disability and to request an accommodation. A decision not to disclose will be respected. Students who request an accommodation must provide appropriate documentation to the Disability Coordinator. The University remains flexible regarding the types of reasonable accommodations that can be made. Students with disabilities are invited to offer suggestions for accommodations.
All members of the University community have the right to learn and work in a safe environment free from all forms of harassment, including harassment on the basis of sex or gender. Students who have been subjected to sexual harassment, including sexual assault, dating/domestic violence or stalking, have the right to receive academic, housing, transportation or other accommodations, to receive counseling and health services and to make a report about such behavior to the University and to law enforcement. For more information please visit www.rochester.edu/sexualmisconduct or contact the Title IX coordinator.