## ME 444 / TME 444:

Continuum Mechanics

####
Department of Mechanical Engineering

University of Rochester

Spring 2019 | Douglas H. Kelley

Lectures 14:00-15:15 Mondays and Wednesdays (Hutchison 138), but not on 18 February, 20 February, 18 March, or 20 March. Make-up meetings 14:00-15:15 on 1 March, 22 March, 29 March, and 5 April (Hylan 203).

CRN 82946 / 82958. Advanced undergraduate students are welcome and can add the course with a paper drop/add form.

#### Course Goals

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.

#### Prerequisites

Basic ordinary and partial differential equations, linear algebra, undergraduate fluid mechanics (ME 225) and solid mechanics (ME 226).

#### Materials

- 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

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 homework — provided that each collaborator takes the time to fully understand the material and write a separate copy of the assignment. On exams, no outside aids are permitted unless the instructor explicitly states otherwise. 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.”

- Homework - 30%
- Roughly one assignment every two weeks. Late homework will not be accepted.
- Midterm - 35%
- 14:00 Monday, 4 March, Dewey 2110E.
- Final exam - 35%
- 14:00 Wednesday, 1 May.

#### Students with Disabilities

The University of Rochester respects and welcomes students of all backgrounds and abilities. In the event you encounter any barrier(s) to full participation in this course due to the impact of disability, please contact the Office of Disability Resources. 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.

#### Feedback & Availability

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, so consider requesting a meeting.

#### Course Sequence

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)