A C1-continuous formulation for 3D finite deformation frictional contact

A new 3D smooth triangular frictional node to surface contact element is developed using an abstract symbolical programming approach. The Cl-continuous smooth contact surface description is based on the six quartic Bezier surfaces. The weak formulation and the penalty method are formulated for the description of large deformation frictional contact problems. The presented approach, based on a non-associated frictional law and elastic-plastic tangential slip decomposition, results into quadratic rate of convergence within the Newton-Raphson iteration loop. The frictional sliding path for the smooth, as well as the simple frictional node to surface contact element presented herein, is defined by the mapping of the current in the last converged configuration. Examples demonstrate the performance of symbolically developed contact elements, as well as the stability and more realistic contact description for the smooth elements in comparison with the simple ones.