Numerical solution procedures for nonlinear elastic rods using the theory of a Cosserat point

The theory of a Cosserat point is developed as a continuum model, which is inherently nonlinear and is valid for arbitrary constitutive equations. Her e, attention is confined to nonlinear elastic response, which is hyperelast ic with a strain energy function, but large displacements, deformations and rotations are allowed. It is shown that the theory of a Cosserat point can be used to formulate a numerical solution procedure for the dynamic three- dimensional motion of nonlinear curved rods by modeling the rod as a set of N connected Cosserat points (like finite elements). Specifically, the Coss erat model allows for axial extension, tangential shear deformation, normal cross-sectional extension, normal cross-sectional shear deformation and ro tary inertia. The Cosserat approach ensures that the global forms of the ba lances of linear and angular momentum are satisfied and the hyperelastic na ture of the constitutive equations is preserved, since the response functio ns are determined by derivatives of a strain energy function. A number of s tatic example problems have been considered, which examine the influence of shear deformation by comparing Cosserat solutions with nonlinear solutions of an elastica. (C) 2001 Elsevier Science Ltd. All rights reserved.