General descriptions of follower forces derived via a geometrically exact inverse contact algorithm

The main feature of the geometrically exact theory of contact is that all objects, which are necessary for computation, weak form and residual, linearized weak form, and tangent matrices are given in a covariant closed form in the local coordinate system corresponding to the geometry of contact pairs. This allows easily to construct computational algorithms for the normal and tangential follower forces as an inverse contact algorithm. In this case, following the definition of the follower forces as given and not changing in the local coordinate system, we have to modify all objects for the contact taking into account the definition of follower forces instead of constitutive relationships for the contact interfaces. The main feature is that the tangent matrices for both normal and tangential part being split into the rotational and the curvature parts are symmetric for any order of approximation. The following numerical examples are selected in the current article to illustrate the effectiveness of implementation: (1) the modeling of a pure bending with a moment applied either as a pair of single forces or a distributed follower forces (pressure) in both 2D and 3D cases; (2) modeling of inflation of a plate as application of the distributed follower normal forces (pressure); and (3) modeling of twisting of a beam with the rectangular cross‐section as application of the tangential follower forces algorithm. Copyright © 2016 John Wiley & Sons, Ltd.