发表机构
Institute for Building Materials, ETH Zurich; Laboratoire de Physique, CNRS, ENS de Lyon, Université de Lyon; Departamento de Física, Universidad de Chile（苏黎世联邦理工学院建筑材料研究所; 里昂高等师范学院物理实验室，法国国家科学研究中心; 智利大学物理系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究脆性软固体在I型平面应变下几何非线性对静态裂纹近尖端场的作用，利用可压缩材料模型分析，通过裂纹尖端开口位移提出后处理方法并推导解析解，定义非线性长度尺度，揭示几何非线性作用，为非线性弹性断裂力学研究提供基础框架。
AI 中文摘要
软弹性固体是高度可变形材料，其断裂由几何和材料非线性的复杂耦合驱动。几何非线性源于固体大变形能力，材料非线性源于材料本构行为。为理解非线性断裂，本文聚焦脆性软固体，在I型平面应变条件下研究几何非线性对静态裂纹近尖端场的单独作用。利用可压缩圣维南 - 基尔霍夫材料模型，分析无材料非线性时大变形下的裂纹行为。提出基于裂纹尖端开口位移轮廓的后处理方法并推导渐近解析解。结果揭示CTOD偏离经典线性弹性预测的独特近尖端区域，过渡到由泊松比决定的非线性区域。定义物理非线性长度尺度$\lambda_{nl}$，表明几何非线性可触发能量分配，有效屏蔽裂纹尖端并赋予明显增韧效果。结论是几何非线性材料模型是更广泛研究非线性弹性断裂力学的基础框架。
英文摘要
Soft elastic solids are highly deformable materials where fracture is driven by the complex coupling of geometric and material nonlinearities. While geometric nonlinearity (GNL) arises kinematically from the intrinsic capacity of solids to undergo large deformations, material nonlinearity stems from the constitutive behavior unique to each class of materials. Because GNL is a universal feature of all highly deformable solids, establishing its standalone impact is a prerequisite for understanding nonlinear fracture. Here, we focus on brittle soft solids to study the role of GNL alone on the near-tip fields of a static crack under mode I plane-strain conditions, providing a canonical baseline for integrating material nonlinearities in future investigations. By utilizing a compressible St. Venant-Kirchhoff material model, we analyze crack behavior under large deformations in the absence of material nonlinearity. We propose a robust postprocessing methodology based on the crack-tip opening displacement (CTOD) profile and derive asymptotic analytical solutions. Our results reveal a distinct near-tip region where the CTOD departs from classical linear elastic predictions, transitioning into a nonlinear regime dictated by Poisson's ratio. Using a matched-asymptotics approach, we define a physical nonlinear length scale $λ_\mathrm{nl}$ that bounds this region and scales quadratically with the far-field stress intensity factor $K_I$. We show that GNL acts as an intrinsic strain-stiffening mechanism sufficient to trigger energy partitioning, effectively shielding the crack tip and imparting an apparent toughening. Ultimately, we conclude that the geometrically nonlinear material model serves as a foundational framework for the broader study of nonlinear elastic fracture mechanics.
