Incremental finite element formulation for large strains based on the nodal force increments

In this paper, we introduce an incremental formulation for large strains which is based on the nodal forces increments. It uses the linear strain increments at the current configuration as the fundamental strain measure, and consequently the stress increments which produce the nodal force increments. It does not assume any total strain and stress calculation according to total values of (large) displacements. It rather employs summation of internal finite element nodal forces during the incremental-iterative computational procedures. Solutions according to this new formulation are compared with a standard updated Lagrangian formulation, with the Green- Lagrangian strains evaluated using the total displacement derivatives with respect to the current reference configurations. The presented incremental-force based formulation can be considered as a generalization of the use of logarithmic strains.