Cosserat Theories: Shells, Rods and Points

Continuum Continuum mechanics mechanics provides provides a a theoretical theoretical structure structure for for analyzing analyzing the the response response of of materials materials to to mechanical mechanical and and thermal thermal loads. loads. One One of of the the beauties beauties of of continuum continuum mechanics mechanics is is that that the the fundamental fundamental balance balance laws laws (conservation (conservation of of mass mass and and balances balances of of linear linear momentum, momentum, angular angular momentum, momentum, energy energy and and entropy) entropy) are are valid valid for for all all simple simple materials. materials. Most Most of of the the modern modern research research in in continuum continuum mechanics mechanics focuses focuses on on the the development development of of constitutive constitutive equations equations which which are are used used to to characterize characterize the the response response of of a a particular particular class class of of materials materials (e.g. (e.g. invisicid invisicid fluids, fluids, viscous viscous fluids, fluids, elastic elastic solids, solids, viscoelastic viscoelastic solids, solids, elastic elastic plastic solids, elastic-viscoplastic solids, etc.). plastic solids, elastic-viscoplastic solids, etc.).

Zusammenfassung
`In conclusion, this is a well-written book that covers important aspects of an area of intensive study in current continuum and structural mechanics research. It is a good example of a modern theoretical treatment of the Cosserat theories of structural mechanics and differs from the few existing books in the field by its focus on the mechanical description of the systems of interest through a more simplified mathematical presentation. The researchers in the field will find an excellent collection of important material in the formulation of these nonlinear theories.'
AIAA Journal, 39:5 (2001)

Inhalt
1 Introduction.- 2 Basic Tensor Operations in Curvilinear Coordinates.- 3 Three-Dimensional Continua.- 4 Cosserat Shells.- 5 Cosserat Rods.- 6 Cosserat Points.- 7 Numerical Solutions using Cosserat Theories.- Appendix A Tensors, Tensor Products and Tensor Operations in Three Dimensions.- A.1 Vectors and vector operations.- A.2 Tensors as linear operators.- A.3 Tensor products (special case).- A.4 Indicial notation.- A.5 Tensor products (general case).- A.6 Tensor transformation relations.- A.7 Additional definitions and results.- Appendix B Summary of Tensor Operations in Specific Coordinate Systems.- B.1 Cylindrical polar coordinates.- B 2 Spherical polar coordinates.- Exercises.- Acknowledgments.- References.