Note that since no constraint has been imposed to the orientation of ei, generally e1·x,1≠0 and thus transverse shear is permitted.
3.3. The small Green–Lagrange strain measure (SGS)
The cross sectional strain measures are obtained from the kinematic assumptions of the blade; it PXD 101 is shown in Ref.  that under the a/f assumptions of Section 2 the small Green–Lagrange strain measure is an excellent choice to describe a large deformation-small strain behavior. Although the kinematic behavior of the blade allows large deformations, the constitutive law of anisotropic materials is only valid for Small strains, and thus for a consistent derivation of the equilibrium equations the use of a small strain measure is sufficient.
Since blades experiment deformation plus rigid body motion, the strain measures must be objective. It was shown in Ref.  that assuming small strains has no consequence in the capability of the large deformation-small strain theory to describe the dynamic response of a beam under this scenario. Moreover, the computational implementation simplifies considerably, so this is the approach that will be followed in this paper. For the sake of brevity only minor details of the derivation of the SGS measure are going to be presented here; for more information the reader should refer to .