Finite element formulations for effective computations of geometrically nonlinear deformations

The paper presents finite element formulations aimed at efficient computation of large geometrically nonlinear flexible body deformations. The formulations are primarily developed for applications in the field of virtual reality technology, but applications in other fields requiring high computational efficiency are also possible. Many applications in the field of virtual reality require real-time or nearly real-time simulation of behaviour of deformable objects, quite often with deformations involving large local rotations. The well-known simplified approach based on mass-spring systems is shortly discussed with advantages and disadvantages pointed out. This is followed by a co-rotational 3D-FEM approach based on rigid-body rotations performed on element level. The approach accounts for large local rotations and yields reasonable accuracy combined with high numerical efficiency. Examples are provided to demonstrate features of proposed formulations.