Session: 06-04-01: Beam, Plate, and Shell Structures

Paper Number: 166473

Topology Optimization of Two-Dimensional Chiral Metamaterials With Mechanical Coupling 

Chiral metamaterials are engineered lattice materials with a chiral micro- or nano-structure, which cannot be imposed onto their mirror transformations by any rotation. These metamaterials have gained increasing attention in recent years due to their ability to adopt mechanical coupling, such as compression–twist and compression–shear coupling, in both 2D and 3D configurations. These mechanical coupling capabilities have led to the development of materials with excellent properties and exceptional functionalities, including auxetic materials with negative Poisson's ratios, robotic materials that mimic living organisms, acoustic cloaks, topological insulators, nonreciprocal elasticity, mechanical activities, and programmable coupling.

There has been a growing interest in developing methods for rational design of chiral metamaterials to achieve prescribed mechanical coupling modes. This design process particularly requires prior understanding of how chiral microstructures influence macroscopic material behaviors and mechanical coupling mechanisms. Essential to this process is the adoption of constitutive models that can accurately represent chiral microstructures and capture their associated mechanical coupling capabilities.

A common approach to investigating mechanical behaviors of chiral metamaterials depends on discrete models that require prior knowledge of chiral structures and their microscopic details. As a result, chiral metamaterials with mechanical coupling capabilities have primarily been designed from discrete, architectured unit cells. However, this approach, while successfully achieving diverse mechanical coupling properties, presents significant limitations in terms of design space and mechanical coupling optimization. Architectured unit cells offer a limited design space, constrained by the specific details of the unit cell’s configuration. Therefore, when optimizing mechanical coupling properties, the shape of the chiral unit cell is preserved throughout the optimization process, thereby curtailing our ability to tailor chiral structures with optimized and customized mechanical coupling properties. Thus, it remains challenging to develop new methods that enable exploring a wide range of chiral unit cells to optimize mechanical coupling properties without being constrained by a specific unit cell shape.

In this study, a novel multi-objective topology optimization approach is developed for designing 2D continuous phononic chiral metamaterials with optimized mechanical coupling properties. This new approach allows optimizing elasticity tensors for continuous metamaterials with  and  symmetries to enable optimized coupling between volumetric dilatational and shear deformations. Initially, the trace of the elasticity tensor is maximized to avoid cases where the material layout has a vanishing bulk or shear modulus. Subsequently, an off-diagonal element of the elasticity tensor is maximized/minimized as the optimization progresses, resulting in a material layout with optimized dilation-shear or shear-shear coupling at the end of the optimization process. This new topology optimization approach represents an efficient method for exploring diverse material configurations that belong to the same material symmetry type, achieving optimized mechanical coupling without being constrained by a specific unit cell shape.

Presenting Author: Mohamed Shaat St. Mary's University

Presenting Author Biography: Dr. Mohamed Shaat is an Assistant Professor of Mechanical Engineering in the Engineering Department at St. Mary’s University. Shaat earned his Ph.D. in Mechanical Engineering from New Mexico State University in 2017. He has held two postdoctoral positions at Southern Methodist University and Boston University, and he was an Assistant Professor of Mechanical engineering at Abu Dhabi University (UAE).
Shaat's research aims at fostering interdisciplinary innovations in advanced materials, manufacturing, quantum science and engineering, and energy storage systems. He applies well-established notions from mechanics and physics to explore new possibilities of harnessing nontraditional phenomena of complex material and engineering systems for various applications. His work on the Mechanics and Physics of Active Matter explores new approaches to understanding and engineering synthetic, biomimetic autonomous materials. Additionally, he exploits the latest advances in machine learning and multi-objective design optimization to optimize electrochemical-based energy storage systems and additive manufacturing technologies.

Authors:

Mohamed Shaat St. Mary's University
Xin-Lin Gao Southern Methodist University