近年來，由于三維制造工藝和優化技術的進步，定制特性的機械材料設計引起了極大的興趣。晶格結構因其高強度–重量比、出色的能量吸收能力和卓越的結構穩定性，在航空航天、汽車、生物醫學和能源系統等領域扮演著不可或缺的角色。

然而，實現具有多種期望力學性能的最優晶格結構的系統設計仍然是一項具有挑戰性的任務。傳統的設計方法依賴于試錯或直覺，可能會耗時、昂貴，而且可能不能保證最佳性能。

制造、有限元分析和優化技術的最新進展擴展了超材料設計的可能性，包括各向同性和拉脹結構，因其獨特的變形機制和在不同載荷下的一致行為而被用于能量吸收等應用。然而，實現多個性質的同時控制，如最佳的各向同性和輔助特性等，仍然具有挑戰性。

Fig. 3 Convergence of the multiobjective optimization process.

來自加州大學伯克利分校機械工程系激光熱實驗室的Timon Meier等，采用全自動多目標設計優化方法，利用遺傳算法優化框架，設計出了具有定制彈性行為的晶格結構。

他們介紹了一種系統的設計方法，將模擬、有限元分析、遺傳算法和優化結合起來，用于創建具有定制力學性能的晶格結構。通過戰略性地排列8種明顯不是各向同性也不是輔助的單位單元狀態，控制了5×5×5立方對稱晶格結構中的剛度張量。

這種設計選擇產生了一個大的違反直覺的組合設計空間，為實現所需的機械性能提供了靈活性。超材料的多光子光刻制造和實驗表征突顯了其現實應用，并證實了理論數據與實驗數據之間的密切關聯。

Fig. 6 Mechanical testing of structures.

作者的方法集成了自動化設計、有限元分析和優化與制造，以及實驗表征，以驗證最優結構，本方法為工程師和研究人員提供了一個有價值的工具，用于創建具有定制的力學性能的晶格結構。該文近期發布于npj?Computational Materials?10:?3 (2023)。

Fig. 7 Experimental compression test data of the optimal structure is presented, along with video captures and a comparison to?theoretical FEA results.

Editorial Summary

The design of mechanical materials with tailored properties has been subject of significant interest in recent years, driven by advancements in three-dimensional manufacturing processes and optimization techniques. Lattice structures, known for their high strength-to-weight ratio, energy absorption capabilities, and structural stability, play an indispensable role in aerospace, automotive, biomedical, and energy systems.?

Fig. 8 Plot illustrating the mechanical compression response of the optimum structure, depicting the relationship between reaction?force and maximum principal stress.

However, achieving systematic design of optimal lattice structures with multiple desired mechanical properties remains a challenging task. Conventional design methods relying on trial and error, or intuition can be time-consuming, costly, and may not guarantee optimal performance. Recent advancements in manufacturing, finite element analysis (FEA), and optimization techniques have expanded the design possibilities for metamaterials, including isotropic and auxetic structures, known for applications like energy absorption due to their unique deformation mechanism and consistent behavior under varying loads. However, achieving simultaneous control of multiple properties, such as optimal isotropic and auxetic characteristics, remains challenging.?

Fig. 9 Directional stiffness map, illustrating the properties of monolithic structures and the optimal structure obtained through the?optimization process.

Timon Meier et al. from the Laser Thermal Laboratory, Department of Mechanical Engineering, University of California, Berkeley, addressed this challenge by employing a fully automated multi-objective design optimization approach using a genetic algorithm optimization framework. In the study, they introduced a systematic design method that combines modeling, FEA, genetic algorithms, and optimization to create lattice structures with customized mechanical properties. Through strategically arranging eight distinctly neither isotropic nor auxetic unit cell states, the stiffness tensor in a 5?×?5?×?5 cubic symmetric lattice structure was controlled. This design choice results in a large counterintuitive combinatorial design space, providing flexibility in achieving desired mechanical properties.?

The application of Multiphoton lithography fabrication (MPL) and experimental characterization of the optimized metamaterial highlights a practical real-world use and confirms the close correlation between theoretical and experimental data. The comprehensive methodology integrates automated design, FEA, and optimization with MPL fabrication, and experimental characterization to validate the optimal structure, offering engineers and researchers with a valuable tool for creating lattice structures with customized mechanical properties.?This?article was recently?published in?npj?Computational Materials?10:?3?(2023).

原文Abstract及其翻譯

Obtaining auxetic and isotropic metamaterials in counterintuitive design spaces: an automated optimization approach and experimental characterization (在反直覺設計空間中獲得拉脹和各向同性超材料：一種自動優化方法和實驗表征)

Timon Meier, Runxuan Li, Stefanos Mavrikos, Brian Blankenship, Zacharias Vangelatos, M. Erden Yildizdag & Costas P. Grigoropoulos

Abstract

Recent advancements in manufacturing, finite element analysis (FEA), and optimization techniques have expanded the design possibilities for metamaterials, including isotropic and auxetic structures, known for applications like energy absorption due to their unique deformation mechanism and consistent behavior under varying loads. However, achieving simultaneous control of multiple properties, such as optimal isotropic and auxetic characteristics, remains challenging.

This paper introduces a systematic design approach that combines modeling, FEA, genetic algorithm, and optimization to create tailored mechanical behavior in metamaterials. Through strategically arranging 8 distinct neither isotropic nor auxetic unit cell states, the stiffness tensor in a 5?×?5?×?5 cubic symmetric lattice structure is controlled. Employing the NSGA-II genetic algorithm and automated modeling, we yield metamaterial lattice structures possessing both desired isotropic and auxetic properties. Multiphoton lithography fabrication and experimental characterization of the optimized metamaterial highlights a practical real-world use and confirms the close correlation between theoretical and experimental data.

摘要?

制造、有限元分析（FEA）和優化技術的最新進展擴展了超材料設計的可能性，包括各向同性和拉脹結構，其獨特的變形機制和在不同載荷下的一致行為而被用于能量吸收等應用。然而，實現多個性質的同時調控，如最佳的各向同性和拉脹特性，仍然具有挑戰性。

本文介紹了一種系統的設計方法，將模擬、有限元分析、遺傳算法和優化結合起來，以在超材料中創造定制的機械行為。通過戰略性地排列8種明顯不是各向同性也不是拉脹元胞態，控制了5×5×5立方對稱晶格結構中的剛度張量。利用NSGA-II遺傳算法和自動化模擬，我們得到了具有期望的各向同性和拉脹性能的超材料晶格結構。優秀超材料的多光子光刻制造和實驗表征突顯了其現實應用，并證實了理論數據與實驗數據之間的密切關聯。