Kinematic Methods for the Rational Design of Mechanical Metamaterials

Most materials around us have properties that are determined at extremely small scales. Often the atoms and molecules that make up these materials determine how they behave under load. While this already leads to a great variety of material properties, a lot more is possible.
Mechanical metamaterials use structure to extend the available range of material properties. In this way, we can design material properties that are not found in nature. An example of this is materials with a negative Poisson’s ratio. When these materials are compressed, they will not expand in the direction perpendicular to the applied deformation, as we would expect from natural materials. Rather, they will contract.
In general, mechanical metamaterials allow us to design materials with properties that are tailored to their intended solution. This provides more design freedom; instead of choosing from a list of available materials, the material properties themselves now become variables that can be designed. Additionally, this makes it possible to integrate multiple functions within a material. In this way, the material is no longer passive but can react based on applied forces, deformations, or changes in the environment.
In practice, designing mechanical metamaterials has turned out to be difficult. While there are many examples of mechanical metamaterials with exceptional properties, their discovery has rarely been based on a rational and structured design process. The lack of such a design strategy makes the design of metamaterials with exactly the desired properties, at least for now, difficult and unreliable.
This dissertation explores this design problem and presents a method to aid in the structured and rational design of mechanical metamaterials. This method is based on a pseudo-rigid body approach, borrowed from the field of compliant mechanisms. Following this approach, the metamaterial is modeled as a collection of rigid parts, which are connected by joints to which we assign a stiffness. This allows us to model both the deformation and the stiffness of the material while keeping the complexity of the models as low as possible.
Because of the limited complexity of the models, this approach allows the designer to understand the effects of design decisions and adaptations. This enables directed and conscious changes to the design, of which the consequences are known beforehand. This is different from alternative methods where highly complex and time-consuming computer models are used to calculate the effects of changes. By using less complex models and making directed choices, new design iterations can be generated more quickly. Especially at the start of a design process, this is expected to quickly lead to new insights. These can then at a later stadium be refined using more detailed methods.