Phase-Field Fracture Simulation of Highly Deformable Thin Structures via a Discrete Differential Geometry Framework
Abstract
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.
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BibTeX
@misc{zhang2026phasefield,
title = {{Phase-Field Fracture Simulation of Highly Deformable Thin Structures via a Discrete Differential Geometry Framework}},
author = {Bohan Zhang and Bo Wang and Huajiang Ouyang and Zhigang Wu and Yu Zhou and Weicheng Huang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.08997},
eprint = {2610.08997},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.08997},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Phase-Field Fracture Simulation of Highly Deformable Thin Structures via a Discrete Differential Geometry Framework
AU - Bohan Zhang
AU - Bo Wang
AU - Huajiang Ouyang
AU - Zhigang Wu
AU - Yu Zhou
AU - Weicheng Huang
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2610.08997
UR - https://arxiv.org/abs/2610.08997
AB - 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.
ER -