发表机构
Northwestern Polytechnical University; Newcastle University; Shenzhen Research Institute of Northwestern Polytechnical University; University of Liverpool; Sun Yat-sen University; Harvard University（西北工业大学; 纽卡斯尔大学; 西北工业大学深圳研究院; 利物浦大学; 中山大学; 哈佛大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种基于离散微分几何的相场框架，用于模拟高变形薄结构的断裂，能准确预测裂纹演化与结构重构，并支持柔性电子器件的损伤容限设计。
AI 中文摘要
薄型弹性柔性结构利用大几何变形来实现机械功能，使其断裂行为与不断演化的结构构型强耦合。本工作提出了一种统一的离散微分几何（DDG）相场框架，用于高变形薄结构中的断裂模拟。膜和弯曲弹性基于三角化中面上的离散几何度量进行公式化，而相场定义在同一离散表面上，以描述裂纹萌生和后续扩展。耦合问题采用交错方案求解，并通过主动集方法强制执行相场不可逆性。一种退化-删除程序移除几乎完全失效的单元并重建DDG拓扑，从而实现完全裂纹张开和显著的断裂后重构。对于二维面内断裂问题，DDG预测在裂纹演化和力学响应方面与几何非线性有限元结果紧密吻合。在三维撕裂中，该框架解析了面外变形与裂纹扩展之间的相互作用，包括实验观察到的初始平行裂纹的汇聚与合并。其工程适用性进一步通过代表柔性电子的岛-桥结构得到展示。模拟捕获了方向相关的变形模式、加载过程中的失稳和突跳，以及结构构型与断裂的耦合演化。这些结果确立了所提框架作为研究几何相关断裂和支持柔性薄结构损伤容限设计的有效工具。
英文摘要
Thin elastic flexible structures exploit large geometric deformation to achieve mechanical functionality, making their fracture behavior strongly coupled with the evolving structural configuration. This work presents a unified discrete differential geometry (DDG) phase-field framework for fracture in highly deformable thin structures. Membrane and bending elasticity are formulated from discrete geometric measures on a triangulated midsurface, while the phase field is defined on the same discrete surface to describe onset of crack growth and subsequent propagation. The coupled problem is solved using a staggered scheme, with phase-field irreversibility enforced by an active-set method. A degradation-deletion procedure removes nearly fully failed elements and reconstructs the DDG topology, enabling complete crack opening and substantial post-fracture reconfiguration. For two-dimensional in-plane fracture problems, the DDG predictions agree closely with geometrically nonlinear finite element results in both crack evolution and mechanical response. In three-dimensional tearing, the framework resolves the interaction between out-of-plane deformation and crack propagation, including the experimentally observed convergence and coalescence of initially parallel cracks. Its engineering applicability is further demonstrated using an island--bridge structure representative of flexible electronics. The simulations capture direction-dependent deformation modes, instability and snap-through during loading, and the coupled evolution of structural configuration and fracture. These results establish the proposed framework as an effective tool for investigating geometry-dependent fracture and supporting the damage-tolerant design of flexible thin structures.
Comments20 pages, 9 figures
