Continuum Mechanics Textbook Talk
I picked up the Lai, Rubin, and Krempl version around 2018 when I was wrestling with finite strain theory for a project on polymer processing. It sits on my desk now next to a copy of Fung that I barely touch. The book is dense but the notation is consistent, which matters more than you might expect when you are reading it at 2am before a seminar. It is published by Butterworth-Heinemann. You can get it from most university bookshops or the publisher directly. The ISBN is 978-0-08-098270-8 for the hardcover. Amazon has it in stock but the pricing swings wildly between semesters. I bought a used copy for about twenty dollars off a grad student who dropped the class. Check the department Facebook group or the campus bulletin board first. The paperback exists but the spine falls apart after six months of being carried around. Buy the hardcover. Your shoulder will thank you.
What the Book Actually Covers
It runs through tensor algebra and calculus first, then moves into kinematics, balance laws, constitutive equations, and elastic/plastic material behavior. The later chapters touch on viscoelasticity and some thermodynamics. It is not a comprehensive reference. If you need detailed treatment of crystal plasticity or phase-field methods, you will outgrow it. But for a first serious exposure to the field, it does the job. One thing the authors do better than most is the treatment of finite strain. They introduce the right Cauchy-Green tensor early and keep coming back to it. I found that approach sticks better than the infinitesimal-first method some other texts use. You can always linearize later. Getting your intuition wrong about large deformations from the start is much harder to fix.
A Problem I Hit With Chapter 5
Chapter 5 covers the stress tensor and the Cauchy principle. The derivation is clean on paper but the example about a curved interface with surface tension tripped me up. The book uses a sign convention for the surface normal that conflicts with the one I had been using from a fluid mechanics course. I spent about an hour going back and forth trying to reconcile the two before realizing the physics was fine and only the bookkeeping was different. The workaround was to draw a free body diagram on graph paper with the actual normal vector labeled, then just map the components directly to the tensor form. Stop trying to memorize the sign rules across different texts. They will kill you. Draw it out every time.
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Common Pitfalls Students Miss
The biggest issue I see is people treating the material derivative like it is just ordinary differentiation. It is not. The convective term shows up in every transport theorem application, and skipping it gives wrong answers on homework that look plausible until you check dimensions. The book derives the Reynolds transport theorem in chapter 3 but students often flip ahead to the constitutive modeling sections without fully working through it. Another trap is the Piola-Kirchhoff stresses. The first and second PK stresses are useful for finite element codes but they do not have the direct physical meaning that the Cauchy stress has. I saw someone on a forum insist that the second PK stress represented actual force per deformed area. It does not. It is force per reference area with a pull-back operation involved. Read the definitions slowly. The indices tell you everything if you actually look at them.
What the Book Does Not Handle Well
The thermodynamics section in the later chapters is thin. If your program requires deep treatment of irreversible thermodynamics or rational thermodynamics approaches, you will need supplementary reading. Gurtin or the Truesdell-Noll papers fill that gap but they are not light evening reading. The book also skims over viscoplasticity and rate-dependent behavior. For metals at high temperature you will want something more detailed. The numerical methods coverage is basically nonexistent. If you need to implement a finite element code for a continuum mechanics problem, this book will not teach you how. There are other texts for that, like Bathe or Hughes. This one is theory-first. That is a feature, not a bug, but it is worth knowing before you buy it expecting code examples.
How I Use It Day to Day
I keep it open on my desk while writing simulation code and reference the stress-strain formulations in chapters 7 and 8 regularly. The eigenvalue treatment of stress invariants comes up when I am checking yield surfaces. I also go back to the polar decomposition sections when I need to separate rotation from stretch in a post-processing step. It is not a book I read cover to cover anymore but having it around saves me from re-deriving standard results under pressure. The appendices with tensor identities are worth using. I printed them out once and taped them inside my laptop case. Still there. Some of the index manipulations you just need to look up rather than derive from scratch during an exam.
Alternatives Worth Knowing
If the notation in Lai Rubin Krempl feels too engineering-heavy, try Malvern. It is more mathematical and slightly older but the derivations are careful. If you want something more applied with more examples, maybe Chen or even a solid mechanics text like Timoshenko for the classical stuff. There is also the newer book by Holzapfel if you are going into biomechanics and need growth and remodeling covered. For free resources, the lecture notes from various universities turn up on GitHub sometimes. I found a set from ETH Zurich a while back that complemented the book well on the continuum thermodynamics side. But those notes vary in quality and coverage so treat them as supplements, not replacements.
Final Practical Note
The exercises are reasonably well graded from straightforward to challenging. Do at least half of them before the semester gets busy. The ones on tensor calculus in the first few chapters are easy points and they pay off later when everything gets abstract. Skipping them because they feel too simple is a mistake I made early on and regretted by midterm. If you are buying this for a course, check the syllabus first to see which chapters are actually assigned. The whole book is not always relevant. Some programs skip the plasticity chapters entirely. Don't waste money on content your professor does not care about.
