Encyclopedia of Continuum Mechanics

Book Preface

Continuum mechanics can be considered as one of the classical branches of mechanics and influences, in a broader sense, all engineering designs and structures of our daily life independent of the scale and taking into account solids and fluids in the same manner. Without a solid foundation in continuum mechanics,it is not possible to master engineering disciplines such as mechanical, civil, or aerospace and engineering progress requires a solid theoretical foundation. In this Encyclopedia, continuum mechanics will be presented focusing on classical theories and new developments. In addition, information on numerical and experimental methods will be provided. For the completeness, some biographical surveys are presented. It seems that continuum mechanics is a purely phenomenological approach, but one can discuss the problems of continuum mechanics on various scales preserving the fundamentals and applying some modifications only. After all, the common starting point for all branches of continuum mechanics is the continuity assumption instead of discrete particles. The state of the art of continuum mechanics is given in thousands of journal papers and various monographs and textbooks. However, with this Encyclopedia the reader will be able to find short articles on continuum mechanics providing a first insight into the complex structure of continuum mechanics and references for further reading. The authors of the entries present their individual point of view and by this the Encyclopedia will stimulate the scientific discourse. Within the Encyclopedia, one receives the minimum required knowledge of continuum mechanics, which means, in the traditional sense, materialindependent and material-dependent equations. In addition to examples of special continua, historical remarks and some topics beyond continuum mechanics like mathematical and numerical methods are included. The internationally recognized team of contributors employs a consistent and systematic approach, offering readers a user-friendly reference that is ideal for frequent consultation. The present Encyclopedia covers most areas of classical and nonclassical continuum mechanics including theoretical, experimental, and numerical aspects. Additional information is given concerning some mathematical tools (e.g., tensor calculus), numerical methods (FEM, BEM), or basic knowledge on material behavior. Any article belonging to continuum mechanics in the narrower sense will follow the structure: material-independent equations (kinematics, loadings, balances) and material-dependent equations characterizing the individual response of the given material on external loadings (constitutive an devolution equations).Finally,for solving practical problems, boundary and initial conditions should be introduced. The Encyclopedia is not restricted to three-dimensional continuum problems and theories. Shells, plates,beams,androds are discussed aswell. In addition,not only mechanical loadings are taken into account that means the influence of temperature, electrical, magnetic, chemical, and other fields in some entries is considered. Several entries present new trends with respect to biological systems. This three-volume Encyclopedia comprises approximately 350 entries now. Please note that it is a “living system” with possible online improvements and extensions anytime. Comments, critical remarks, etc. are highly appreciated. The editors will do their best to make the Encyclopedia better and better. At the same time, an extension will be realized systematically. We would like to express our since reappreciation to all the authors ,section editors, and the representatives of Springer, who made this major reference work in mechanics possible.

Magdeburg, Esslingen, Germany Holm Altenbach November 2019 Andreas Öchsner