An explicit finite element formulation for very large deformations based on updated material reference frame

An explicit finite element formulation which has the capability of handling very large geometrical changes is developed. The formulation is based on an updated material reference frame and hence a true stress-strain test can be directly applied to properly characterize properties of materials which are subjected to very large deformations. For the large deformations, a consistent formulation based on the continuum mechanics approach is derived. The kinematics is referred to an updated material frame. Body equillibrium is also established based on the updated geometry. The second Piola-Kirchhoff stress tensor and the updated Lagrangian strain tensor are used in the formulation. Numerical examples of frame structures are solved to validate the presented formulation and to demonstrate the importance of imposing material properties properly.