Auxetic structure design using compliant mechanisms: A topology optimization approach with polygonal finite elements

Compliant mechanisms are monolithic structures where the movement is given by the flexibility of the structure rather than the presence of joints and pins. The absence of joints allows the construction of compliant mechanisms in microscale. In this work, the compliant mechanism is designed by using topology optimization to generate microstructure unit cells that simulate the effect of auxetic materials, i.e. those with negative Poisson's ratio. Polygonal finite element meshes are introduced in the topology optimization formulation to avoid the hinges (one-node connections) in the compliant mechanism design. A pattern repetition constraint is applied to generate auxetic macrostructures. An integrated approach that combines a projection technique with a mapping technique is adopted to include the minimum member size constraint, making the topology optimization results possible to be manufactured. The connection of the topology optimization approach with additive manufacturing is demonstrated using 3D printers based on FFF (fused filament fabrication) and PolyJet technologies. Thus, computational simulation in connection with rapid prototyping are carried out to verify the results.