## Victor Saouma Ecublens Juin

PREFACE

One of the most fundamental question that a Material Scientist has to ask him/herself is how a material behaves under stress, and when does it break. Ultimately, it its the answer to those two questions which would steer the development of new materials, and determine their survival in various environmental and physical conditions.

The Material Scientist should then have a thorough understanding of the fundamentals of Mechanics on the qualitative level, and be able to perform numerical simulation (most often by Finite Element Method) and extract quantitative information for a specific problem.

In the humble opinion of the author, this is best achieved in three stages. First, the student should be exposed to the basic principles of Continuum Mechanics. Detailed coverage of Stress, Strain, General Principles, and Constitutive Relations is essential. Then, a brief exposure to Elasticity (along with Beam Theory) would convince the student that a well posed problem can indeed have an analytical solution. However, this is only true for problems problems with numerous simplifying assumptions (such as linear elasticity, small deformation, plane stress/strain or axisymmetry, and resultants of stresses). Hence, the last stage consists in a brief exposure to solid mechanics, and more precisely to Variational Methods. Through an exposure to the Principle of Virtual Work, and the Rayleigh-Ritz Method the student will then be ready for Finite Elements. Finally, one topic of special interest to Material Science students was added, and that is the Theoretical Strength of Solids. This is essential to properly understand the failure of solids, and would later on lead to a Fracture Mechanics course.

These lecture notes were prepared by the author during his sabbatical year at the Swiss Federal Institute of Technology (Lausanne) in the Material Science Department. The course was offered to second year undergraduate students in French, whereas the lecture notes are in English. The notes were developed with the following objectives in mind. First they must be complete and rigorous. At any time, a student should be able to trace back the development of an equation. Furthermore, by going through all the derivations, the student would understand the limitations and assumptions behind every model. Finally, the rigor adopted in the coverage of the subject should serve as an example to the students of the rigor expected from them in solving other scientific or engineering problems. This last aspect is often forgotten.

The notes are broken down into a very hierarchical format. Each concept is broken down into a small section (a byte). This should not only facilitate comprehension, but also dialogue among the students or with the instructor.

Whenever necessary, Mathematical preliminaries are introduced to make sure that the student is equipped with the appropriate tools. Illustrative problems are introduced whenever possible, and last but not least problem set using Mathematica is given in the Appendix.

The author has no illusion as to the completeness or exactness of all these set of notes. They were entirely developed during a single academic year, and hence could greatly benefit from a thorough review. As such, corrections, criticisms and comments are welcome.

Finally, the author would like to thank his students who bravely put up with him and Continuum Mechanics in the AY 1997-1998, and Prof. Huet who was his host at the EPFL.

## Post a comment