On the dynamics of flexure and stretch in the theory of elastic rods
A theory of planar motions of straight elastic rods is presented where the strains are assumed to remain small, although displacements and rotations may be large. It is a specialization of the Kirchhoff-Clebsch theory without the usual assumption of inextensibility, i.e., of temporal invariance of arc length. Its origin as an approximation to the theory of nonlinearly elastic slender bodies is discussed, various alternative formulations of the theory are presented, and a list of conservation laws is given. Then, after discussing the general theory of traveling waves, the authors analyze in detail solitary waves and noninflexional as well as inflexional waves. In particular, it is shown that under some conditions supersonic traveling-wave solutions may be rejected as inadmissible, i.e., not physically meaningful.
theory of nonlinearly elastic slender bodies
scientific article; zbMATH DE number 760205