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


利用战略性设计的二维 (2D) 前体结构进行柔性电子器件的三维 (3D) 屈曲组装，由于其对各种长度尺度和高性能材料的多功能适用性，已在各个领域实现了重要应用，以及丰富多样的 3D 拓扑。允许将 3D 介观结构直接映射到未知的 2D 前体结构和加载参数上的合理设计方法是这些组装技术的基础，但面临着科学挑战，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式 3D 介观结构/电子器件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模具辅助组装策略，作为可定制独立式 3D 细观结构和电子产品的新途径。结合力学建模、有限元分析和实验测量，可以清楚地了解双层带状网络在 2D 到 3D 转换过程中的非线性弯曲-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，为曲率规划提供了理论基础。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）和仿生 3D 弯曲带和介观表面（例如，模仿波浪藤蔓、硅藻和任意​​卷曲的叶子）被逆向设计并通过实验实现。能够进行应变/温度传感和微型 LED 指示的设备演示表明了其在生物电子学和微机电系统中的应用机会。