Towards real-time simulation of deformable structures by means of co-rotational finite element formulation

Whereas typical Finite Element (FE) computations are performed off-line, many virtual-reality (VR) applications put a demand for interactive simulations involving deformable objects. Interactive simulation implies real-time or nearly real-time computation and graphical representation of modeled deformable objects. The growing computational power of modern conventional hardware calls for FEM developments in this direction. Depending on specific VR applications, the developments need to account for different aspects of physical behavior, with geometrically nonlinear deformations emerging as one of most important and frequent. This paper proposes a simplified co-rotational FE formulation that considers the overall finite element motion as a superposition of rigid-body rotation and deformation described by a linear model with respect to the co-rotated reference frame. By neglecting the stress stiffening effect and the dependence of the element stiffness matrix on the deformational displacements, the formulation aims at meeting the objectives of highly efficient simulation, under certain conditions even real-time simulation, and with acceptable deviation in accuracy compared to the rigorous nonlinear FE formulation. Computations with both solid and shell elements are addressed. A set of examples is provided to illustrate and discuss the aspects of accuracy and achievable simulation speed.