textbooks

Here are the chapter names:

1) Prototypes of the theory of elasticity and viscoelasticity

2) Tensor analysis

3) Stress tensor

4) Analysis of strain

5) Conservation Laws

6) Elastic and plastic behavior of materials

7) Linear elasticity

8) Solutions of problems in elasticity by potentials

9) Two-dimensional problems in elasticity

10) Variational Calculus, energy theorems, saint-venant's principle

11) Hamilton's principle, wave propagation, applications of generalized coordinates 

INTRODUCTION TO TENSOR CALCULUS and CONTINUUM MECHANICS

John H. Heinbockel

Very clear treatment on tensors and vector calculus, also free online!

http://www.math.odu.edu/~jhh/counter2.html

Amazon Review

Chapters:

Despite the title, the book covers very little specifically on geology.  It works through stress, strain, and other tensor quantities, but assumes you know little about the math.  Fully worked problems make up the bulk of the book following a few introcutory chapters.  I've found it a nice review of the math, but haven't fully explored the solution sections.  I got the book from Cabot Science Library here at Harvard. I wouldn't recommend buying it on amazon it's not worth the $72, but it is a nice addition to Timoshenko's theory of elasticity.

• Amazon.com reviews 
• Content (by chapter):
• Stress
• Strain
• Mechanical Properties of Materials
• Axial Load
• Torsion
• Bending
• Transverse Shear
• Combined  Loadings
• Stress Transformation
• Strain Transformation
• Design of Beams and Shafts
• Deflections of Beams and Shafts
• Buckling of Columns
• Energy Methods

I registered for iMechanica a few days ago, and found many postings instructive. Here is my first blog entry.

The topics being studied today by mechanicians are very difficult (what I often call "dirty problems"). In fact, often the mechanical theories (actually coupled mechanics, biology, chemistry) required to gain improved understanding are still in their infancy. Mechanicians that have entered fields such as mechanics of biological structures have gotten up to speed by paying the price (hopefully an enjoyable time on a learning curve) of reading large numbers of papers and discipline-based books. Many of these papers are cryptic and, while they may be of high scientific quality, they do not have significant pedagogical value to those entering the field (graduate students for example).

Though not that original, I want to recommend Timoshenko. Since many people have mentioned it already, I will discuss a Brief on Tensor Analysis by James Simmonds. Though not always useful, I sometimes use it to remember tensor rules that I have forgotten. The book is divided into chapters as follows:

I: Vectors and Tensors

II: General Bases and Tensor Notation

III: Newton's Law and Tensor Calculus

IV: Gradient, Del Operator, Covariant Differentiation, Divergence Theorem

Again, sometime it is not that useful and you spend your time trying to read it while not learning much, but it does come in handy sometimes. You can see the amazon link:

Amazon

I would like to recommend "Elasticity: Theory, Applications, and Numerics" by Prof. Martin H. Sadd as a reference for ES240. The book, as its name indicated, is mainly focused on elasticity theory and its applications, but also discusses numerical methods such as finite element method and boundary element method.

Prof. Martin H. Sadd, organized the book into two parts: I. foundations, and II Advanced topics. In part I, the book clearly outlines the basic equations of elasticity, i.e. strain/displacement relation, Hooke's law, and equilibrium equation. The other context of part I is devoted to the formulation and solution of two-dimensional problems. This structure matches the progress of our class very well.

The second part of the book begins with the discussion of anisotropic elasticity, thermo-elasticity, and micromechanics. These topics are complementary to the notes of ES240, and helpful in solving homework problems. In its last chapter, the book introduced finite element method and boundary element method.