A Sequential two-step design framework for deformable mechanical metamaterials

Deformable metamaterials are materials that are made up of several repeating elastic building blocks whose geometries can be tailored to obtain a specified global shape change or stiffness behavior. They are deemed useful in soft robotics, shape morphing mechanisms, stretchable electronics, wearable devices, and devices that adapt according to their environment. This paper presents a two-step sequential design framework for the synthesis of deformable mechanical metamaterials where (a) topology optimization is used to map global deformation requirement to local elasticity matrix, followed by (b) a selection of building block microstructure geometry from a database and refining it to match the elasticity requirement. The first step is accomplished through a unique parameterization scheme that enables the classification of the planar orthotropic elasticity matrix into four distinct classes. The second step uses a kinetostatic framework known as load flow visualization to populate candidate microstructure geometries within these four classes. Finally, the framework is validated for the design of a cantilever beam with a specified lateral stiffness requirement and the design of planar sheets that exhibit sinusoidal deformation patterns..