Designing Shape Morphing Behavior through Local Programming of Mechanical Metamaterials

Shape morphing implicates that a specific condition leads to a morphing reaction. The material thus transforms from one shape to another in a predefined manner. In this paper, not only the target shape but rather the evolution of the material's shape as a function of the applied strain is programmed. To rationalize the design process, concepts from informatics (processing functions, for example, Poisson's ratio (PR) as function of strain: ν = f(ε) and if-then-else conditions) will be introduced. Three types of shape morphing behavior will be presented: (1) achieving a target shape by linearly increasing the amplitude of the shape, (2) filling up a target shape in linear steps, and (3) shifting a bulge through the material to a target position. In the first case, the shape is controlled by a geometric gradient within the material. The filling kind of behavior was implemented by logical operations. Moreover, programming moving hillocks (3) requires to implement a sinusoidal function ε_y  = sin (ε_x ) and an if-then-else statement into the unit cells combined with a global stiffness gradient. The three cases will be used to show how the combination of mechanical mechanisms as well as the related parameter distribution enable a programmable shape morphing behavior in an inverse design process.