Page 13 - Introduction to Continuum Mechanics

Preface to the Third Edition

The first edition of this book was published in 1974, nearly twenty years ago. It was written
as a text book for an introductory course in continuum mechanics and aimed specifically at the
junior and senior level of undergraduate engineering curricula which choose to introduce to
the students at the undergraduate level the general approach to the subject matter of
continuum mechanics. We are pleased that many instructors of continuum mechanics have
found this little book serves that purpose well. However, we have also understood that many
instructors have used this book as one of the texts for a beginning graduate course in continuum
mechanics. It is this latter knowledge that has motivated us to write this new edition. In this
present edition, we have included materials which we feel are suitable for a beginning graduate
course in continuum mechanics. The following are examples of the additions:

1. Am'sotropic elastic solid which includes the concept of material symmetry and the
constitutive equations for monoclinic, orthotropic, transversely isotropic and isotropic
materials.

2. Finite deformation theory which includes derivations of the various finite deformation
tensors, the Piola-Kirchhoff stress tensors, the constitutive equations for an incompres-
sible nonlinear elastic solid together with some boundary value problems.

3. Some solutions of classical elasticity problems such as thick-wailed pressure vessels
(cylinders and spheres), stress concentrations and bending of curved bars.

4. Objective tensors and objective time derivatives of tensors including corotational
derivative and convected derivatives.

5. Differential type, rate type and integral type linear and nonlinear constitutive equations
for viscoelastic fluids and some solutions for the simple fluid in viscometric flows.

6. Equations in cylindrical and spherical coordinates are provided including the use of
different coordinates for the deformed and the undeformed states.
We wish to state that notwithstanding the additions, the present edition is still intended to
be "introductory" in nature, so that the coverage is not extensive. We hope that this new
edition can serve a dual purpose: for an introductory course at the undergraduate level by
omitting some of the "intermediate level" material in the book and for a beginning graduate
course in continuum mechanics at the graduate level.

W. Michael Lai
David Rubin
Erhard Krempl
July, 1993

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