RENEWAL AND CHANGE OF FRAME IN FINITE DEFORMATION

The present paper describes the theoretical aspects of the renewal and a change of coordinate system in finite deformation. The proposed renewal method is accomplished through mathematically equivalent transformation of the fundamental work equations derived from the total Lagrangian approach. Since no subsidiary condition is imposed on the transformation, it is proven that the variational principle and the constitutive equation can be treated as an independent problem. Discussed are the relative advantages of the total or updated Lagrangian approaches as well as the Green or Jaumann rate constitutive equations from the viewpoint of numerical analysis. Attention is also focused on the work theorems and the constitutive equation to ensure objective numerical integration under the change of frame.