A formulation of arbitrarily shaped surface elements for three-dimensional large deformation contact with friction

The paper introduces a general theory for the numerical simulation of large deformation contact problems. The contacting bodies under consideration may be of two- or three-dimensional shape modelled by nite elements. A contact nite element which can be applied to handle multi-body contact as well as contact with rigid bodies is developed. The element is universal in the sense that it can be used as a surface element for any known nite element model and includes friction. The frictional behaviour of the model obeys Coulombʹs law of friction distinguishing between sticking and sliding contact. The algorithmic treatment is based on a penalty formulation for the normal and sticking contact. The corresponding consistent tangential sti ness matrices are derived, leading to an overall quadratic convergence behaviour for the method. This feature is demonstrated in a number of representative examples