Nonlinear solid mechanics a continuum approach for engineering pdf

Gerhard Holzapfel. Download PDF. A short summary of this paper. Meccanica —, Printed in the Netherlands. ISBN: Holzapfel is facilitated by his own preface, where both the aims and the approaches of the book are outlined, showing a clear overview of the material.

For a reader who likes to have a concise basis of criticism it is worthwhile to state that this book is really outstanding because it fills a space in the scientific literature for all those who want to master the essential principles and related mathematical tools that govern the nonlinear behaviour of solids. In the personal library of a scientist or of a scholarly student the book can be placed close to classical textbooks of solid mechanics such as those by Malvern or Gurtin, to which it is comparable in its approach and high level of culture shown.

Holzapfel is a civil engineer who teaches courses at Graz University of Technology, and he is a well-known scientist in theoretical and computational biomechanics.

The combination of such expertise forms the basis for the original character of the book, which can be summarized as an excellent com- promise between exactness, completeness and comprehensibility. The formulations presented are introduced within a mathematical framework appropriate to the up-to-date topics central to materials engineering and bioengineering.

These two areas, which demand the strong culture of nonlinear solid mechanics, are implicit scenarios within the book even if they are not treated directly because a too wide extension would have been necessary. So, the didactic mission is twofold: the former is that declared by the author, namely giving the student a comprehensible tool, well conceived with respect to both definition, notation and algebra of vectors and tensors, and numerous worked examples; the latter focus is on the goal which should be the prime purpose of any textbook, and it is accomplished by this book in an ex- cellent and very effective way.

Once familiar with the main ideas the reader will be able to specialize in different aspects of the subject matter. I felt the need for a self-contained textbook intended primarily for beginners who want to understand the correspondence between nonlinear continuum mechanics, nonlinear constitutive models and variational principles as essential prerequisites for finite element formulations.

Of course, no single book can cover all aspects of the broad field of solid mechanics, so that many topics are not discussed here at all. The selection of the material for inclusion is influenced strongly by current curricula, trends in the literature and the author's particular interests in engineering and science. Here, a particular selection and sty le was chosen in order to highlight some of the more inspiring topics in solid mechanics.

I hope that my choice, which is of course subjective, will be found to be acceptable. My ultimate intention was to present an introduction to the subject matter in a didactically sound manner and as clearly as possible. I hope that the text provides enough insights for understanding of the terminology used in scientific state-of-the art papers and to find the 'right and straightforward path' in the scientific world through the effective use of figures, which are very important learning tools.

They are designed in orderIX. Necessary mathematics and physics are explained in the text. The approach used in each of the eight chapters will enable the reader to work through the chapters in order of appearance, each topic being presented in a logical sequence and based on the preceding topics. A proper understanding of the subject matter requires knowledge of tensor algebra and tensor calculus. For most of the derivations throughout the text I have used symbolic notation with those clear bold-faced symbols which give the subject matter a distinguished beauty.

However, for higher-order tensors and for final results in most of the derivations I have used index notation, which provides the reader with more insight. Terminology is printed in bold-face where it appears for the first time while the notation used in the text is defined at the appropriate point.

For those who have not been exposed to the necessary mathematics I have included a chapter on tensor algebra and tensor calculus. It includes the essential ideas of linearization in the form of the concept of the directional derivative. Chapter 1 summarizes elementary properties which are needed for the vector and tensor manipulations performed in all subsequent chapters and which are necessary to many problems that arise frequently in engineering and physics.

It is the prime consideration of Chapter 2 to use tensor analysis for the description of the motion and finite deformation of continua. The continuum approach is introduced along with the notion 'Lagrangian' material and 'Eulerian' spatial descriptions.

In a systematic way the most important kinematic tensors are provided and their physical significance explained. The push-forward and pull-back operations for material and spatial quantities and the concept of the Lie time derivative are introduced. The concept of stress is the main topic of Chapter 3. Cauchy's stress theorem is introduced, along with the Cauchy and first Piola-Kirchhoff traction vectors, and the essential stress tenso. Forces and stresses 4.

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