The critical role of the base curve for the qualitative behavior of shearable rods

Stuart S. Antman and Friedemann Schuricht

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Submission date: 25. Sep. 2001
Pages: 23
published in: Mathematics and mechanics of solids, 8 (2003) 1, p. 75-102 
DOI number (of the published article): 10.1177/1081286503008001766
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Abstract:
This paper treats several aspects of the induced geometrically exact theory of shearable rods, of central importance for contact problems, for which the regularity of solutions depends crucially on the presence of shearability. (An induced theory is one derived from the 3-dimensional theory by the imposition of constraints. Because the role of thickness enters into our theory in an essential way, it is an exact version of what has been called the theory of "moderately thick" rods.) In particular, we study how the theory and constitutive restrictions depend upon the choice of the base curve, and we show how this choice has major qualitative consequences, which are illustrated with several concrete examples.