Real-time simulation of deformable structures by means of conventional hardware tools: Formalisms and applications

Interactive simulation of deformable objects has recently become increasingly significant in various applications ranging from entertainment industry to virtual reality simulators and to engineering tasks in the field of Multi-Body System (MBS) dynamics. Simulation at interactive frame rates implies real-time or nearly real-time computation and graphical representation of modelled deformable objects. Though various approaches have been addressed in the past few decades, the Finite Element Method (FEM) has deservedly established itself as the method of choice for general deformable structures. Typical engineering tasks are resolved using the so-called off-line" FEM computations. However, the growing computational power of modern hardware has enabled FEM developments for real-time simulations. Depending on specific applications, the developments need to account for different aspects of structural behaviour. One of the most frequent requirements is the nonlinear structural behaviour, primarily the geometrically nonlinear deformation. This paper gives an overview of our developed FEM formalisms with the objective of enabling highly efficient, interactive simulations with geometrical nonlinearities included. The formalisms range from mass-spring systems to modal-space based solutions and co-rotational FEM formulations for solids and shells. Techniques employed to reduce the numerical burden in order to meet the objectives are discussed together with the time-integration schemes and solvers chosen to resolve dynamics of the system. A set of interactive examples is provided to illustrate different formalisms and the wide range of their applicability.