On the material symmetry of elastic rods. (English) Zbl 0976.74036

Luo, Cheng; O’Reilly, Oliver M.

J. Elasticity 60, No. 1, 35-56 (2000).

Summary: This paper presents a treatment of material symmetry for hyperelastic rods, where the rod theory is based on a Cosserat (or directed) curve with two director fields. Two material symmetry groups are discussed: one pertains to the strain-energy function, while the other pertains to the response functions. The paper closes by showing how the treatment relates to the form-invariant approach used in A. E. Green and P. M. Naghdi’s papers [see, e.g., Int. J. Solids Struct. 15, 829-853 (1979; Zbl 0419.73004)] and a treatment proposed recently by H. Cohen [Meccanica 31, No. 5, 527-546 (1996; Zbl 0884.73028)].

MSC:

74K10	Rods (beams, columns, shafts, arches, rings, etc.)
74B20	Nonlinear elasticity

Keywords:

Cosserat theory of rods; material symmetry; hyperelastic rods; strain-energy function; response functions; form-invariant approach