Three-dimensional (3D) buckling assembly of flexible electronics from strategically designed two-dimensional (2D) precursor structures has enabled important applications in a variety of areas, owing to its versatile applicability to a broad range of length scales and high-performance materials, as well as to a rich diversity of 3D topologies. Rational design methods that allow direct mapping of 3D mesostructures onto unknown 2D precursor structures and loading parameters are foundational to these assembly technologies, but face scientific challenges, such as the high nonlinearity of spatial deformations and tricky bifurcation behaviors. While a few inverse design methods based on the beam theory, topology optimization and machine learning algorithms have been reported, the shape programming of freestanding 3D mesostructures/electronics with highly complex curvature distributions remains elusive. In this work, we propose a curvature programming method based on bilayer ribbon networks, along with a mold-assisted assembly strategy, as a new route to customizable freestanding 3D mesostructures and electronics. Combined mechanics modeling, finite element analyses and experimental measurements allow a clear understanding of nonlinear bending-stretching coupled deformations of bilayer ribbon networks during the 2D-to-3D transformation. A parameter domain with one-to-one mapping of the dimensionless curvature and the bending stiffness ratio is identified, offering a theoretical basis of the curvature programming. By introducing a discretization strategy, a variety of regular (e.g., circles, ellipses, spirals and toroids) and biomimetic 3D curved ribbons and mesosurfaces (e.g., mimicking wavy vines, diatoms and arbitrarily curled leaves) were inversely designed and experimentally realized. A device demonstration capable of strain/temperature sensing and micro-LEDs indication suggests application opportunities in bioelectronics and microelectromechanical systems.

中文翻译：

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基于双层带状网络的独立式 3D 介观结构和柔性电子器件的曲率编程


由战略设计的二维 （2D） 前驱体结构对柔性电子设备进行三维 （3D） 屈曲组件，由于其对广泛的长度尺度和高性能材料以及丰富多样的 3D 拓扑结构的通用适用性，使其在各个领域都实现了重要应用。允许将 3D 介观结构直接映射到未知的 2D 前驱体结构和加载参数的合理设计方法是这些装配技术的基础，但面临科学挑战，例如空间变形的高度非线性和棘手的分叉行为。虽然已经报道了一些基于梁理论、拓扑优化和机器学习算法的逆向设计方法，但具有高度复杂曲率分布的独立 3D 介观结构/电子设备的形状编程仍然难以捉摸。在这项工作中，我们提出了一种基于双层带状网络的曲率编程方法，以及一种模具辅助装配策略，作为可定制的独立 3D 介观结构和电子学的新途径。结合力学建模、有限元分析和实验测量，可以清楚地了解二维到 3D 转换过程中双层带状网络的非线性弯曲-拉伸耦合变形。确定了无量纲曲率和弯曲刚度比一对一映射的参数域，为曲率编程提供了理论基础。通过引入离散化策略，各种规则（例如，圆形、椭圆形、螺旋线和环形线）和仿生 3D 弯曲带状和中间表面（例如，模仿波浪形的藤蔓、硅藻和任意卷曲的叶子）是逆向设计和实验实现的。能够进行应变/温度传感和 micro-LED 指示的器件演示表明了在生物电子学和微机电系统中的应用机会。