A new linearized expression for strain increment in finite-element analyses of deformations involving finite rotation (Q1073633)

It is demonstrated that large errors will arise unless the strain increment used in the formulation of the stiffness of elements undergoing large plastic deformation is independent of material rotation. The infinitesimal expression, which is normally used in nonlinear incremental finite-element analyses of metal forming processes, is shown to be grossly inaccurate even when the incremental rotation of the workpiece is small. A new expression for incremental strain is presented which is a linear function of incremental-displacement gradients and which gives values that are in excellent agreement with those measured in the rotating frame of reference for a wide range of incremental strains and rotations. The new expression may easily be incorporated in existing finite-element treatments.