Topology optimization of multi-material negative Poisson's ratio metamaterials using a reconciled level set method

63Citations
Citations of this article
132Readers
Mendeley users who have this article in their library.

Abstract

Metamaterials are defined as a family of rationally designed artificial materials which can provide extraordinary effective properties compared with their nature counterparts. This paper proposes a level set based method for topology optimization of both single and multiple-material Negative Poisson's Ratio (NPR) metamaterials. For multi-material topology optimization, the conventional level set method is advanced with a new approach exploiting the reconciled level set (RLS) method. The proposed method simplifies the multi-material topology optimization by evolving each individual material with a single level set function and reconciling the result level set field with the Merriman–Bence–Osher (MBO) operator. The NPR metamaterial design problem is recast as a variational problem, where the effective elastic properties of the spatially periodic microstructure are formulated as the strain energy functionals under uniform displacement boundary conditions. The adjoint variable method is utilized to derive the shape sensitivities by combining the general linear elastic equation with a weak imposition of Dirichlet boundary conditions. The design velocity field is constructed using the steepest descent method and integrated with the level set method. Both single and multiple-material mechanical metamaterials are achieved in 2D and 3D with different Poisson's ratios and volumes. Benchmark designs are fabricated with multi-material 3D printing at high resolution. The effective auxetic properties of the achieved designs are verified through finite element simulations and characterized using experimental tests as well.

Cite

CITATION STYLE

APA

Vogiatzis, P., Chen, S., Wang, X., Li, T., & Wang, L. (2017). Topology optimization of multi-material negative Poisson’s ratio metamaterials using a reconciled level set method. CAD Computer Aided Design, 83, 15–32. https://doi.org/10.1016/j.cad.2016.09.009

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free