A comprehensive kinematic model of single-manifold Cosserat beam structures with application to a finite strain measurement model for strain gauges

Abstract

In this paper, we investigate the coupling of Poisson’s and warping effect for a general asymmetric cross-section of Cosserat beam. We present the challenges and inconsistencies observed as a result of our attempt to couple the two effects. The fully-coupled Poisson’s transformation is then developed to describe the in-plane deformation for the prismatic beam. A comprehensive kinematic treatment of geometrically exact and nonlinear Cosserat beam subjected to large deformation and finite strain is finally obtained that extensively captures the deformation due to multiple curvatures, torsion, shear, axial deformation, warping and a fully-coupled Poisson’s effect in the cross-section, all while maintaining the single manifold nature of the problem. The contributions to the strain vector and the deformation gradient tensor due to various deformation effects are interpreted and explained in detail. In the final part of the paper, we use the kinematics developed to establish a measurement model of discrete and finite length strain gauges attached to the surface of the beam (or embedded into the beam). We investigate the relationship between the scalar strain measurement of the strain gauge and the local finite strain parameters of the beam.