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# Let's compare notes: first graduate courses in solid mechanics

This semester I teach an introductory graduate course in solid mechanics. Following a suggestion made by Mark Walter, I posted an outline of my course in iMechanica.

This is the first time I teach the course at Harvard, but I taught a similar course at UCSB, and an upper-level undergraduate course of similar content at Princeton. The students for the three courses have different backgrounds. At Harvard, I assume that students have taken an undergraduate course on strength of materials (tension, bending, torsion, etc.), a course on multi-variable calculus, and a course on linear algebra. I try to avoid excessive math, and try to bring out features of mechanics. (My students may disagree with me, but at least my heart is in right place.) Most students will not be specialized in mechanics, as evident from their descriptions of themselves.

Many of us teach a similar course at different universities. It might be fun and useful for us to compare notes. Could you please describe your introductory graduate course in solid mechanics? For example, you can list topics, textbooks, and backgrounds of students. If you already posted notes online, please include a hyperlink.

You can post your description of the course as a comment to this forum entry. Alternatively, you can post a blog entry, and then enter a brief comment below this forum topic, with a hyperlink pointing to you blog entry.

Related discussion on a post by Roberto Ballarini:

Are notes and textbooks a higher priority than journal clubs?

## The first introductory

The first introductory graduate course in solid mechanics at University of Houston is "Theory of Elasticity". Professor Lewis Wheeler teaches it but I will jot down a few details here on his behalf.

Zhigang, like the students your describe, our students typically have no more advanced background than a strength of materials type course. Lewis has developed his own set of notes on this subject. There is heavy emphasis on mathematical structure which turns out to be quite useful in that students rapidly "grow up" from undergraduates to researchers who can read the literature in mechanics.

Personally, the first course I taught when I joined UH (Spring 2004) was "Nanomechanics of Materials". For my research group I still regard it as an introductory course; the only pre-requisite being a course in either continuum mechanics or elasticity. I do not use a book and I have created my own notes. When I teach it again (most likely Spring 2008), I will clean them up and post them online.

In this course, after reviewing classical continuum mechanics, I use Eshelby's inclusion problem as both an entry into micromechanics and to illustrate several concepts: (i) use of green's functions (ii) size-independency of classical continuum mechanics (iii) coarse graining aka homogenization and (iv) the famous "cutting & welding" thought experiments useful for so many other applications. (v) defects

Once done with this introductory part (which is essentially applied or advanced elasticity), I discuss the physical causes that may lead to the breakdown of classical elasticity and the associated mathematical framework. This involves discussion of Gurtin/Murdoch's formulation of surface/interfacial elasticity, nonlocal and higher order continuum theories, non-affine elasticity etc. I present several applications to the study of nanostructures.

The next half of the course can be best characterized as "condensed matter physics for mechanical engineers". Here I try to introduce quantum mechanics, some basics of solid state physics such as concept of phonons, band structure etc. After this I provide a survey of atomistic methods including analytical calculations of elastic moduli, surface and defect energies using simple pair or EAM potentials.

Due to the time constraints this course ends up being a lot broader than deep but seems to have provided most of the students enough of a start to read research literature on their own.

## Your course on condensed matter physics for mechanical engineers

Pradeep: Thank you for a quick and detailed response. Hopefully this forum will be useful for us teaching the course, and for graduate students to gain a broader perspective.

I also hope one day to see Lewis's notes and your notes posted in iMechanica! A colleague here commented the other day that he wished Bernie Budiansky had left his lecture notes behind. Bernie was a brilliant teacher, and I still go back to the notes I took when I was student in his classes (solid mechanics 1, solid mechanics 2, shells). But it would surely be different if notes were written by him. We all miss him.

## Introductory course in solid mechanics at Berkeley

Shaofan Li has just posted an entry on his course at Berkeley.

## my first graduate course in solid mechanics

Before I talk about teaching, I thought of classes I took as a student. The first graduate mechanics course I took at Princeton University was

Continuum Mechanics, taught by Professor Peter C.Y. Lee. Before that, coming from a five-year undergraduate program in mechanics at Univeristy of Science and Technology of China (USTC), I had many mechanics courses such aselasticity,plasticity,vibrations, etc. (Unfortunately, this mechanics program has changed significantly during the last ten years and is now a usual four-year program.) Even better, I had a few graduate courses at USTC, including one onContinuum Mechanics. With all these, I had little trouble at Princeton, as far as the courses were concerned. Still, I learned a great deal in my second take onContinuum Mechanicsat Princeton, which was quite intense in terms of mathematics. For one thing, it put all the mechanics I learnt before into one unified framework, and suddenly, it made a lot more sense to me when talking about stress and strain. However, I believeContinuum Mechanicsis no longer fitting as the first graduate course in solid mechanics for most graduate programs in the United States, simply because we have (almost) no undergraduate program specialized in mechanics.Now at Univerisity of Texas at Austin, I find that we have to teach many mechanics courses at the graduate level, partly because we maintain a fairly big graduate program in

Engineering Mechanics(unlike Zhigang's class, many students in our graduate classes are expected to specialize in mechanics). A entering graduate student typically takes 3 classes,Advanced Strength of Materials(a undergraduate elective),Solid Mechanics I(officially, the first graduate course) andSolid Mechanics II, before he takesContinuum Mechanics. I taughtSolid Mechanics Iin Fall 2005. Compared to Zhigang's outline, we did not go very far. Essentially, we covered only the first two items:elements of elasticityandplane elasticity problems. The syllabus of this course can be found from my webpage, and an outline is given below. Maybe I can post more information when I get chance to teach this course again. I believe that all the other items in Zhigang's list are covered in other courses of our graduate curriculum. An interesting question however is: which way is more efficient in educating our future mechanicians?A course outline for

Solid Mechanics I,University of Texas at Austin:RH

## First graduate course in solids

This year, I am also teaching a new graduate course in solid mechanics. It's the first in a sequence of two classes that the students majoring in solids need to take. I have been updating the syllabus during the semester but the major topics that we cover are:

I am using the new book by Asaro & Lubarda and notes.

## Advanced Mechanics of Solids

At Columbia I teach the first graduate class of solid mechanics. Before, the class focused on advanced beam theory since there were also senior undergraduate students taking this class, plus the students mostly came from Civil Engineering. In recent years, only highly motivated and exceptional undergraduate students would consider to take this course, and there are more students from mechanical and biomedical engineering. Thus I changed the course to a more conventional first year solid mechanics course, which covers Basic tensor analysis. Stress and equilibrium. Strain and displacement. Constitutive relations. Boundary value problems for linear elastic solids. Torsion and bending. Plane problems and simple 3D problems. Variational methods.

I try to not cover too many areas but explain the derivation of governing equations in detail, plus lots of examples. Among all classic textbooks I have looked into, I prefer the Chinese textbook "elasticity" by Keh-Chih Hwang and I developed notes based on that. Also I found John Hutchinson's notes on ES240 very helpful. The only English textbook I found having the similar content and focus is "Elasticity: Theory, applications, and numerics", by M. H. Sadd, 2005, Elsevier, and I have asked the students to use it as an optional textbook for 2 years. The book misses some details yet it's a good choice for the 1st year graduate course.

## Continuum mechanics

I took the continuum mechanics course this semester. It is really very interesing and helpful. But only 4 students took the course. The Professor clearly explained what was expected in material. She does not look at classnote in class. All the derivation and fomular are at hand when she instructs. I think this course not only improves my ability to explain basic concepts/principles in mechanics but also cultivate us with a thought on how to think.

## Video lectures on linear elasticity

Anyone have any good websites that link to video lectures in elasticity. I am currently taking a graduate level course & the lecturer is a bit lacking in sufficient mathematical details in solving the problems. Our final is in 2 weeks & I thought I could augment my studies via some other online lectures.

appreciate any info, my email jberg3@unl.edu