Multi-Material Topology Optimization using a

Reconciled Level-Set Method

Topology optimization with Reconciled Level-Set method is applied to designing metamaterials with negative Poisson’s ratio. In this method, each material is being represented by a single level-set function and evolves separately utilizing the Merriman-Bence-Osher (MBO) operator. The problem is formulated as a least square optimization problem minimizing the difference between the effective properties and the design targets, under a volume constraint. The effective properties are obtained through the Strain Energy Method, an alternative to homogenization method with a relatively simpler and efficient way to implement. The sensitivity analysis, utilizing the adjoint variable method, is carried out in order to construct the design velocity field. The final obtained design is a unit cell that can be assembled periodically to form a metastructure with the negative Poisson’s ratio behavior. This method has been used to obtain both 2D and 3D multi-material designs.

3D multi-material negative Poisson’s ratio design using Reconciled Level-Set Method

Merriman-Bence-Osher operator for Reconciled Level-Set Method in action

2D multi-material negative Poisson’s ratio design using Reconciled Level-Set Method

Volume constraints:                   45% for the hard material, and 15% for the soft one.

Poisson’s ratio: ν=-0.36

Representative publications:

Journal:

Panagiotis Vogiatzis, Shikui Chen, Xiao Wang, Tiantian Li, and Lifeng Wang, “Topology Optimization of Multi-Material Negative Poisson’s Ratio Metamaterials Using a Reconciled Level Set Method.” Computer-Aided Design, 83 (2017): 15-32.

Shikui Chen, Stefano Gonella, Wei Chen, and Wing Kam Liu. "A level set approach for optimal design of smart energy harvesters." Computer Methods in Applied Mechanics and Engineering 199, no. 37 (2010): 2532-2543.

Conference:

Panagiotis Vogiatzis and Shikui Chen, “Topology Optimization of 3d Auxetic Metamaterials Using Reconciled Level-Set Method”, ASME Proceedings of IDETC/CIE, August 21-24, 2016, Charlotte, North Carolina, USA.

Xiao Wang, Shikui Chen and Lei Zuo, “On Design of Mechanical Metamaterials Using Level-Set Based Topology Optimization”, ASME Proceedings of IDETC/CIE, August 2–5, 2015, Boston, Massachusetts, USA.

Demonstration