A direct stiffness-modification approach to attaining linear consistency between incompatible finite element meshes

In this work, a method is proposed for modifying the standard master-slave stiffness matrix so that linear consistency across the interface of the master and slave meshes is achieved. The existence of such a local stiffness modification is implied by the work of [Dohrmann, et al, to appear]. The present work aims at achieving the same linear consistency through a different method of stiffness modification that is based on simply ensuring zero residual force at the interior interface nodes for all non-zero-stress linear displacement fields and zero residual force at all interface nodes for all rigid-body linear displacement fields. These zero residuals ensure that the local stiffness modification results in an interface that passes the patch test. Numerical examples herein demonstrate that the maximum stress error at the interface goes to zero with the proposed method while it does not for the standard master-slave method