负泊松比负热膨胀超材料微结构拓扑优化设计

Topology Optimization Design of Microstructured Metamaterials with Negative Poisson's Ratio and Negative Thermal Expansion

提出一种拓扑优化设计方法,用于设计同时具有负泊松比和负热膨胀系数的超材料.超材料是人工设计的复合材料,由微米或纳米结构的周期性阵列组成,并具有天然材料难以具备的超常物理性质.基于拓扑优化理论,建立了一个表示多材料微观结构的多相边界的水平集模型,并采用数值均匀化方法来计算微观结构的等效性能,然后通过参数化水平集优化方法实现边界形状的演变和拓扑结构的设计.通过两个数值算例,给出超材料微结构材料分布的优化结果,证明了设计方法的可行性,为实现具备特殊性能的人工材料设计提供了一套系统的设计方法.

A level set-based method was introduced to design the metamaterials which can exhibit negative Poisson's ratio and negative thermal expansion simultaneously.Negative Poisson's ratio(also called auxeticity)and negative thermal expansion are phenomena that may rarely be found in the nature materials.It is now known that these unusual properties are mainly dependent on the particular features in the material's micro-or nano-structural deformation when subjected to a thermal or mechanical load.A numerical homogenization method was applied to evaluate the effective properties of the microstructure,and the multi-phase level set method was used to implement the shape and topology evolutions of the microstructure.Two numerical examples were given to demonstrate the feasibility of the proposed topology optimization method,which provides a systematic design method for the design of artificial materials with special properties.