The Special Cosserat Theory of Rods
In this chapter we generalize the development of Chap. IV by formulating the general dynamical theory of rods that can undergo large deformations in space by suffering flexure, torsion, extension, and shear. We call the resulting geometrically exact theory the special Cosserat theory of rods. In Sec. 2 we outline an honest derivation of the governing equations for elastic and viscoelastic rods. Here we scarcely pause for motivation, interpretation, and justification of our results. The purpose of this presentation is twofold: to establish a framework for the ensuing careful treatment in subsequent sections and to demonstrate that there is a short and pleasant path leading from fundamental physical principles to the governing equations. Armed with these results, the reader interested in the treatment of concrete problems is ready to begin the following chapter. A full appreciation of the theory, however, requires a study of the topics covered in the remainder of the present chapter, which also serves as an easy entrée into ideas important for three-dimensional theories of solids.
KeywordsConstitutive Equation Rigid Motion Reference Configuration Transverse Isotropy Constitutive Function
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