Continuum Mechanics: Advanced Topics and Research Trends

R In the companion book (Continuum Mechanics Using Mathematica )to this volume, we explained the foundations of continuum mechanics and described some basic applications of ?uid dynamics and linear elasticity. However, deciding on the approach and content of this book, Continuum Mechanics: Advanced Topics and Research Trends, proved to be a more di?culttask.Afteralongperiodofre?ection,wemadethedecisiontodirect our e?orts into drafting a book that demonstrates the ?exibility and great potential of continuum physics to describe the wide range of macroscopic phenomena that we can observe. It is the opinion of the authors that this is the most stimulating way to learn continuum mechanics. However, it is also quite evident that this aim cannot be fully realized in a single book. Consequently,inthis book wechoseto presentonly thebasicsofinteresting continuum mechanics models, along with some important applications of them. We assume that the reader is familiar with all of the basic principles of continuum mechanics: the general balance laws, constitutive equations, isotropygroupsfor materials,the laws of thermodynamics, ordinarywaves, etc. All of these concepts can be found in Continuum Mechanics Using Mathematica and many other books. We believe that this book gives the reader a su?ciently wide view of the “boundless forest” of continuum mechanics, before focusing his or her attention on the beauty and complex structure of single trees within it (- deed,wecouldsaythatContinuumMechanics UsingMathematica provides only the fertile humus on which the trees of this forest take root!).

This book offers a broad overview of the potential of continuum mechanics to describe a wide range of macroscopic phenomena in real-world problems. Building on the fundamentals presented in the authors’ previous book, Continuum Mechanics using Mathematica®, this new work explores interesting models of continuum mechanics, with an emphasis on exploring the flexibility of their applications in a wide variety of fields.

Specific topics, which have been chosen to show the power of continuum mechanics to characterize the experimental behavior of real phenomena, include:

* various aspects of nonlinear elasticity, including equilibrium equations and their variational formulation, nonlinear constitutive equations, existence and uniqueness theorems of Van Buren and Stoppelli, and Signorini's method with some extensions to live loads and acceleration waves
* continua with directors
* a model of a continuum with a nonmaterial moving interface
* mixture theory: The Gibbs Rule in a binary mixture
* interaction between electric or magnetic fields with matter
* micromagnetism
* continua in special relativity and relativistic interactions between matter and electromagnetic fields

Appendices are included to provide background information on topics such as surface geometry, first-order PDEs, and weak solutions to models. Mathematica® notebooks also accompanying the text are available for download at http://www.birkhauser.com/978-0-8176-4869-5.

Aimed at advanced graduate students, applied mathematicians, mathematical physicists, and engineers, the work will be an excellent self-study reference or supplementary textbook in graduate-level courses focusing on advanced topics and research trends in continuum mechanics.