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

• Published in: Computer aided design Vol. 83; pp. 15 - 32
• Main Authors: Vogiatzis, Panagiotis, Chen, Shikui, Wang, Xiao, Li, Tiantian, Wang, Lifeng
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Ltd 01.02.2017; Elsevier BV
• Subjects: Boundary conditions; Design; Dirichlet problem; Elastic properties; Finite element method; Functionals; High resolution; Metamaterial; Metamaterials; Multi-material; Negative Poisson’s ratio; Properties (attributes); Reconciled level set method; Steepest descent method; Strain; Three dimensional printing; Topology optimization; Topology optimization; Negative Poisson’s ratio; Reconciled level set method; Metamaterial; Multi-material
• ISSN: 0010-4485; 1879-2685
• DOI: 10.1016/j.cad.2016.09.009

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. •A multi-material topology optimization approach exploiting the reconciled level-set method.•The boundary of each individual material is evolved with a single level set function.•Multiple level set functions are reconciled with the Merriman–Bence–Osher (MBO) operator.•Both 2D and 3D multi-material designs were obtained and used for validate the proposed method.