A note on tangent stiffness for fully nonlinear contact problems

In the numerical solution of geometrically nonlinear contact problems by the finite element method, it is often assumed that the modification to the tangent stiffness takes the form of the single rank‐one‐update characteristic of the linear theory. It is shown that due to the kinematic nonlinearity such a simple structure no longer holds. Within the context of the discrete problem arising from a finite element formulation, explicit expressions for the residual and the tangent stiffness matrix are obtained for both penalty and Lagrangian parameter procedures.