Embedded homogeneity of beams in the nonlinear domain

The notion of embedded homogeneity of thin-walled structures is introduced as the property characterizing the provenance of such a structure from a homogeneous material. This property needs to be distinguished from other definitions of homogeneity formulated exclusively in terms of a purely structural constitutive equation. Necessary conditions for embedded homogeneity are derived for planar beams and their geometric interpretation is expressed as the condition for the elastic hodograph to lie on a hypersphere containing the origin of a six-dimensional space of tensors.