Metamaterials are materials that are engineered to possess extremal properties, often not found in nature, such as negative Poisson's ratio, negative thermal expansion coefficient, high modulus, etc. Mechanical metamaterials that deform are deemed useful in soft robotics, shape morphing mechanisms, wearable devices, and devices that adapt according to their environment. Despite the advantages, deformable mechanical metamaterials are not easy to design as there is no systematic design framework that preserves the intuition of the designer while delegating the tedious task of optimization to a computer.  Methodologies to design deformable mechanical metamaterials in literature can be broadly classified into insightful and computational approaches. Insightful methods are one-off rational designs obtained from the intuition of the designer. These methods are problem-specific and are challenging to extend to other design requirements such as shape-matching, stiffness, or stress requirements. Computational approaches such as structural topology optimization and reconciled level sets are mathematically robust to handle a wide range of design requirements. Yet, they are time-consuming and sensitive to the algorithms used and may provide limited designer insights. Furthermore, the solutions obtained may require extensive post-processing to be practical and manufacturable.  

In this paper, we present an alternative two-step systematic design framework for the synthesis of deformable mechanical metamaterials, using a kinetostatic formulation that enables visualizing load flow in the metamaterial geometry. Load flow provides functional insight into the different structural building blocks that make up the microstructure geometry. Strain-energy based homogenization method maps the local material microstructural geometry to global material properties. The paper presents a qualitative database that classifies the entire planar orthotropic design space using load flow visualization into four classes: (a) positive Poisson's ratio microstructures with high shear, (b) positive Poisson's ratio microstructures with low shear, (c) negative Poisson's ratio microstructures with high shear and (d) negative Poisson's ratio microstructures with low shear. With a database of feasible microstructures in each qualitative class, the paper aims to determine the best topological combination of these microstructural building blocks that achieves a desired kinematic or stiffness requirement. 

The proposed framework involves two sequential steps. In the first step, we obtain conceptual designs by performing material optimization on the design domain with a parameterized elasticity matrix. The obtained conceptual solutions are chosen from a database of feasible microstructures. And in the second step, we perform a shape-size refinement, where the preselected microstructure geometry is fine-tuned to exactly meet the desired kinematic or stiffness requirements. This process provides the designer with control of the creative part of the design process. At the same time, the more tedious shape-size refinement is performed in the second step by computationally efficient algorithms. Finally, the framework is validated with three design examples. The first example is of a cantilever beam with stiffness requirements, and the other two examples are of a planar sheet with desired kinematic requirements of sinusoidal shape-matching.


A Sequential Two-Step Design Framework for Deformable Mechanical Metamaterials

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Aerospace, Bioengineering, Applied Mechanics, Design Engineering Division, Advanced Energy Systems, Manufacturing Engineering Division, Noise Control and Acoustics, Nondestructive Evaluation, Diagnosis, and Prognosis (NDPD), Nuclear Engineering Division, Process Industries Division, Fluids Engineering, Heat Transfer, Materials, Microelectromechanical Systems, Safety Engineering and Risk Analysis, Computers & Information in Engineering


Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2020/volume/84478

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