Abstract Gradually stiffer (GS) mechanical metamaterial is a novel kind of adaptive structures under nonlinear varying loads for cushioning and vibration damping in engineering. These man-made metamaterials in applications are usually tailored by trial-and-error. This study develops a design framework that integrates the topology optimization, parametric design and compression experiment for the GS mechanical metamaterials induced by the negative Poisson's ratio (NPR) property. Firstly, a parametric level set method is incorporated with the numerical homogenization method to topologically optimize a series of microstructural unit cells with different NPRs. Then, the nonlinear static analysis is respectively applied to different unit cells to check their GS behavior. Secondly, typical microstructures with GS property are selected and simplified to perform the subsequent parametric design to analyze the expected property. Thirdly, the obtained mechanical metamaterials are fabricated by using the additive manufacturing (AM). GS properties of the obtained designs are analyzed and verified by both the simulation and compression experiments. Results show that we could obtain the GS mechanical metamaterial based on NPR properties for their similar characteristics. This study demonstrates that the proposed design framework is effective to tailor innovative layouts of the GS mechanical metamaterials.

中文翻译：

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由负泊松比特性引起的逐渐变硬的机械超材料的设计框架

摘要 渐增刚性（GS）机械超材料是一种在非线性变化载荷下用于工程缓冲和减振的新型自适应结构。这些应用中的人造超材料通常是通过反复试验来定制的。本研究开发了一个设计框架，该框架集成了由负泊松比 (NPR) 特性引起的 GS 机械超材料的拓扑优化、参数化设计和压缩实验。首先，将参数水平集方法与数值均质化方法相结合，对一系列具有不同 NPR 的微观结构单元进行拓扑优化。然后，将非线性静态分析分别应用于不同的晶胞以检查它们的 GS 行为。第二，选择并简化具有 GS 特性的典型微观结构，以执行后续参数化设计以分析预期特性。第三，获得的机械超材料是通过使用增材制造（AM）制造的。通过模拟和压缩实验分析和验证了所获得设计的 GS 特性。结果表明，我们可以获得基于 NPR 特性的 GS 机械超材料，因为它们具有相似的特性。该研究表明，所提出的设计框架可有效定制 GS 机械超材料的创新布局。通过模拟和压缩实验分析和验证了所获得设计的 GS 特性。结果表明，我们可以获得基于 NPR 特性的 GS 机械超材料，因为它们具有相似的特性。该研究表明，所提出的设计框架可有效定制 GS 机械超材料的创新布局。通过模拟和压缩实验分析和验证了所获得设计的 GS 特性。结果表明，我们可以获得基于 NPR 特性的 GS 机械超材料，因为它们具有相似的特性。该研究表明，所提出的设计框架可有效定制 GS 机械超材料的创新布局。