  Inclusion of contact in mechanical designs opens a large range of design
possibilities, this includes classical designs with contact, such as gears,
couplings, switches, clamps etc. However, incorporation of contact in topology
optimization is challenging, as classical contact models are not readily
applicable when the boundaries are not defined. This paper aims to address the
limitations of contact in topology optimization by extending the third medium
contact method for topology optimization problems with internal contact.
  When the objective is to maximize a given contact load for a specified
displacement, instabilities may arise as an optimum is approached. In order to
alleviate stability problems as well as provide robustness of the optimized
designs, a tangent stiffness requirement is introduced to the design objective.
To avoid a non-physical exploitation of the third medium in optimized designs,
small features are penalized by evaluating the volume constraint on a dilated
design. The present work incorporates well-established methods in topology
optimization including Helmholtz PDE filtering, threshold projection, Solid
Isotropic Material Interpolation with Penalization, and the Method of Moving
Asymptotes. Three examples are used to illustrate how the approach exploits
internal contact in the topology optimization of structures subjected to large
deformations.
