Stress, Strain and Moduli

Since both of my major projects as well as my coursework are hitting on the subject this week, I though I'd talk about elastic moduli. However, before I can talk about that, we need to talk a bit about stress, strain and the concept of anisotropy.

Stress is fundamentally defined as force per unit area. Strain is the change in length per unit length. In a Cartesian coordinate system (which we use unless we're doing pipes or spheres), this means that to fully describe the stress and strain in three dimension, we end up with matrices.

Stress is typically written as σ, while strain is ε (we use them for conductivity and dielectric constants too...). By combining our two matrices according to the generalized Hooke's Law , we end up with a fourth-order tensor, Cijkl which we call the stiffness tensor. We can also invert the relationship and get Sijkl which is the compliance tensor. I think every mechanics of materials professor ever wishes the symbols on these two were reversed, but we're stuck with the convention of C=stiffness and S=compliance. 


Now we get to the idea of anisotropy, which is the concept that materials don't behave the same in all orientations. For a perfectly isotropic material (like liquid), the strain response will be the same regardless of direction. In this case, the number of independent elastic constants drops to two: Young's modulus and Poisson's ratio. Young's modulus is also known as the modulus of elasticity, while Poisson's ratio describes the degree to which a materials expands in the unconstrained directions when compressed in the third.  In an anisotropic material, these values are no longer constants, but instead become matrices as well. 


My current research nemesis is the bulk modulus, which is particularly challenging to determine using experiments or simulations. It can either be determined from the derivative of the pressure-volume relationship or the derivative of the pressure-density relationship. In both cases, relaxation and equilibration are critical to minimize scatter in the data. However, reality being what it is, you usually end up with at least some scatter, and can consequently get some crazy derivatives depending on the method you chose for defining the slope at each point.


Bulk modulus is also unique in terms of the anisotropy question: other moduli measure response to a linear stress, be it axial or shear. Bulk modulus describes the compressibility of a material under isotropic pressure, and therefore, the value of the bulk modulus isn't a directional dependent thing. Which is kind of cool. It still makes me want to bang my head on a wall right now, though.

Elbow Patches

After 6 hours of reading papers, I realize why the classic professorial tweed jacket has leather patches on the elbows. I could use some padding there right now...

Invisible Skills

Over the last few days, I've been helping one of the students in my lab edit his thesis (grammar, not content). It's been a collective effort of the group, with several of us working on different chapters. Through this process, I've discovered that I am apparently much faster at it than my native English speaking peers.

I know roughly when I picked up this skill. In high school, I was a grader for freshman English for 2 years, and I graded chemistry lab reports for 2 years as well (there was some overlap in there...). I had just never before realized that I was particularly good at it.

What skills do you have that you didn't realize you were acquiring until much later?

Kitten Update

Since I'm currently watching code compile, a quick update.

After his needle-eating adventure, the kitten is doing pretty well. He's getting used to taking pills, and the stitches are healing nicely. I still don't understand how the vet expects us to make sure our kitten is "less active". The most acrobatic thing he does is chase his own tail, and we can't exactly hide that from him. He looks so tragic when we won't play, but hopefully after the stitches come out this weekend, we'll be back to normal (other than being much more diligent about putting thread where he can't eat it...)

No segmentation faults yet...

Hours vs. Productivity

During graduate recruitment visits the last two weekends, several questions consistently come up. Some of them make sense. Why did we (the grad students), pick GiantU besides the ranking? What is [insert professor] like? Can I live in GiantUTown without a car?

Questions that make less sense to me are things like: Where else did we apply? How long does it generally take to graduate? (This one is a very advisor-dependent question...)

The one question that came up more than I expected was this: does [insert professor] expect you to be in the lab on weekends?

Here's the thing: most professors in my department really don't care which hours you work. In some groups, it is expected that *someone* will be working every weekend. Generally, this is because there's one particular piece of equipment everyone needs to use, and so in order for everyone to get things done efficiently, someone will end up in the lab on the weekend. On the other hand, even for the most hard-core experimentalist, there is always work you can get done without actually being in the lab. Literature searches, data analysis or writing up results all immediately leap to mind.

I don't understand professors (at least in engineering, where we don't generally need to keep things alive) who expect their students to keep specific minimum hours. I can be in the office for 14 hours a day, but somewhere after the 11th hour, I stop being very productive. If I'm working on multiple projects, I can often work for longer. But I can only work continuously on the same problem so long.

Do you have a productivity threshold for a single task, or can you just work almost indefinitely on a problem, given enough food and caffeine?

Silly kitten...

Today is going to be a rough one. The kitten decided around 10 last night that he should eat one of my sewing needles, and we weren't able to fish it out before he swallowed it. So little kitten (who isn't so little anymore) got rushed off the the emergency clinic to get the needle surgically removed before it did any real damage.  Needless to say, I made it to bed rather later than normal.

Oh, plus I have two exams today.  Yep.

Science versus Engineering: Understanding the Ampersand

MS&E occupies a slightly odd space in the STEM spectrum, typically associating itself with both science and engineering. So what is the difference between the two, and how does MS&E encompass both?

Science asks why: at a fundamental level, why do materials behave in specific ways? Why is diamond harder than graphite? Science often asks questions for the sake of knowing the answer. There may not be an immediately useful application for something, but that's not the real point of science.

Engineering asks what, when and how: what should I use to build this, when will it fail, and how to I maximize the usefulness of my widget? Engineering takes science and uses it to make and improve things. In the absence of a fundamental explanation, though, engineering makes an empirical model and tweaks it until it is "good enough".

Materials science and engineering departments typically cover a spectrum between "pure science" (e.g., theoreticians) and "pure engineering" (e.g. process development ). But most of what we do lands somewhere in the middle. Quantum studies of structures are often done in line with an experimental group developing fuel cells, or synthesizing organic electronic materials, or studying failure in composites. Creep studies tie back to fundamental diffusion theories from statistical mechanics.

Of course, there's another, more pragmatic reason for the "and engineering". Materials scientists involved in failure analysis projects often get their PE certification to testify as expert witnesses. For many B.S. students, their ultimate jobs will have titles like "Quality Engineer" or "Production Engineer", working on the factory floor. And there's also the idea of ABET certification. There's no clear process of accreditation of science departments, to the best of my knowledge. Being able to say you have an accredited degree opens up international opportunities, and gives departments a way to quickly convey to prospective undergraduates that they will receive a solid education.

Realistically, at the post-bachelor level, all engineering drifts towards the "why" type of questions. Without those questions and answers, we're left with trial and error as a mean of improving our systems. There is certainly something to be said for just doing something, and seeing what happens. On the other hand, being able to make predictions from fundamental knowledge can save time and money in development. Materials science is just a bit more explicit about the union.

Halfway there..

One weekend of recruiting down without incident. Very very few students met with my advisor, which I think is more due to the very practical leanings of the first group of visitors. There was a lot of interest in the possibilities of jobs in industry, rather than a single-minded focus towards academia. Even though we do some experimental research, it's not something that immediately leaps out as being very practical, nor is my advisor very good at conveying it as such.

Despite all of my courses dumping projects on me at once, I'm finally feeling a little productive over in research land. As much as I know literature review is an important part of the whole thing, it just never feels quite as productive as actually writing/running code.

Rain

Today has been one of those rainy days where I just want to be at home, reading, with the cat on my lap. (Or trying to eat my hair. He's still very kittenish.)

  I've at least got the reading part down...

Learning Linguistics

I've always been interested in languages and how the way your language is constructed affects how you think. One of my favorite things about grad school is having linguistics conversations with non-native speakers, especially about idioms and grammatical constructions. Explaining how passive voice works in English is a particularly fun challenge. Why and where do you use proper nouns? And how do you respond to "What's up?"

My first language is English, and I sort of know Spanish (when I can remember enough vocabulary). Once upon a time, I started learning German, and then my school dropped the program. Structurally, there are some major differences between the languages. The use of gendered nouns is one big difference between English and other European languages. Spanish also conveys the degree of formality in both the pronoun and verb conjugation. English also deals with tenses more simply. [Disclaimer: going from memory here]. There's past, present, and future. Spanish is more specific, with immediate past, general past, present, specific future, general future, and past future (would have been, basically). 100 Years of Solitude makes much more sense in Spanish, where non-linear time is much more easily accommodated linguistically.

I realized recently that the amount of time I spend in conversation with non-native speakers has changed some of my habits. I'm more precise in my word choice than I used to be, and my diction is no longer quite as Midwestern-neutral as it was in high school. I occasionally get asked if I ever lived in England (which I haven't, I just watch too much BBC).

English is a complex, messy language with few consistent rules. It steals from everyone. It's incredibly colorful and nuanced, and very subject to cultural interpretation. There's a huge volume of assumed connotation with word choice, and this is part of what makes it so incredibly difficult to learn. I have to remind myself of this occasionally, and remember that scientific papers should be read for content.

The failure to use proper nouns correctly does not affect the quality of the science, but it is certainly distracting.

Being honest, but not too honest...

My department has graduate student recruit visits for the next two weekends. While I'm not involved in planning this year, I like being involved. Given my current advisorial issues, this raises a dilemma. How do I sell the department when I'm a bit bitter about how things have turned out for me?

Harder still is how honest to be in answering questions about my advisor. He's a nice guy, we do interesting work (I really love my project), and when he eventually manages to give feedback, it's generally constructive. On the other hand, funding for the experimentalists has been flaky of late, and his snail-like response times aren't likely to vanish overnight.

We also have a large fraction of the group defending within the next year (1/2 of the non-postdocs). It wouldn't be a bad thing for the group to get a bit smaller, but we will need another experimentalist soon (we'd be down to one lonely student). The only new student we got this year switched groups to join us, rather than being a new enrollee.

I think at this point, I plan to answer questions honestly, but I'm not going to volunteer negative information. The important part is convincing them that GiantU is a good place to be. Advising decisions don't have to be set until well into the fall semester. We've just gotten two new postdocs, and they may have some positive effects on group dynamics by then.

Hooky?

Grad school: when leaving the office after an 8 hour day during spring break when your advisor is on another continent feels like playing hooky.

What do you mean it's still light out?

Favorite Classes vs. Favorite Teachers

Over at Engineer Blogs , there's a lovely discussion on people's favorite classes. For me, this is a slightly tricky question, even if I only restrict it to college courses. My favorite course was not from my favorite teacher.

My favorite class was a "humanities" course (taught be a civil engineering prof, hence the quotes). This was one of the university general requirement courses, and was meant to be a critical writing course on a particular subject. My section discussed failure. Over the course of the semester, we were to develop a class definition of failure, while analyzing a number of engineering and societal failures. There were two books for the class: Why Things Break, by Levy and Salvadori, and Collapse, by Jared Diamond. Part of what made the class my favorite was relating engineering concepts to things one wouldn't typically consider engineering problems, like the collapse of society on Easter Island.

My favorite teacher, on the other hand, taught my Intro to Materials and my Thermodynamics classes. He was by no means the most dynamic lecturer I've ever had, but his lecture style made it very easy to grasp the material for a variety of learning styles. Intro to Materials is a giant lecture, so he had to use power point just so it would be legible in the back of the room. Whenever he was going through equations, he would flip to the document camera and do the math there.

Thermo was a much smaller class, and he could do everything on the boards. The most amazing thing was they way he would write everything down while talking. He never lectured faster than you could take notes, because he was taking them on the board. He also would use one phrasing out loud, and write down a different wording. For some classes, this wouldn't be a big deal. Thermodynamics (Statistical Mechanics for physics majors), on the other hand, can be conceptually tricky, and different wordings click with different people. It's not my favorite class ever, because will very well taught, it's just not particularly fun for most people. He did, however, deliver my favorite professorial quote ever:

With enough coefficients, you can curve-fit an elephant.

Pseudonymous Naming Schemes

Since I'm not blogging under my actual name, I've decided I need a cute naming scheme for everything (because I can!).

Undergrad institution: Since GEARS has dibs on SnowU, I'll call mine SnowTech. Unless he's in Alaska, or SnowU actually is SnowTech, I'm pretty sure we got more snow...

Grad institution: I'm now at a very large R1 university, henceforth to be known as GiantU

Significant Other: I'll be marrying Mr. ME this summer. He's a mechanical engineer at a large manufacturing company (we'll call them Employer) with an obsession for cars, Doctor Who and and our kitty. The kitty, by the way, is named Kitten. We attempted to give him an actual name, but pretty much failed.

Periodic Boundary Conditions: While my undergraduate program was very much based in classical metallurgy, my current research is in atomistic computational simulations. In order to make the system seem larger, periodic boundary conditions are critical, where if an atom tries to move out of the simulation box, it will reappear on the opposite face, making our solid effectively infinite (assuming you start with a decent sized box). I'll attempt to come up with how that's a metaphor for life later.

... and now back to reading papers.  Woo.

You know you're an engineer when...

You use a Gantt chart to help plan your wedding. We're behind our target, but we were deliberately ambitious with our time line planning to give ourselves a nice buffer.

Watching other friends panicking about planning, I'm thankful that 1) I'm marrying an engineer  2) my parents are also engineers and 3) most of the wedding party is engineers (except my sister the architect). Good engineers have a fundamentally different approach to problem solving that is much less stressful for event planning. There's no "oh noes, everything is ruined!!11!!!" mentality. However, there might be an excessive habit of fixing things with duct tape...