发表机构
Michigan State University; University of Wisconsin - Madison; University of Delaware（密歇根州立大学; 威斯康星大学麦迪逊分校; 特拉华大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对软材料等离散载荷传递的晶格网络，构建离散裂纹尖端理论，揭示其双区域裂纹尖端标度律，经光弹性水凝胶实验验证，为预测链变形与固有断裂能提供框架。
AI 中文摘要
裂纹尖端场控制着变形局域化与破坏起始，经典连续介质断裂力学通过Hutchinson-Rice-Rosengren（HRR）场等理论描述幂律非线性固体中的这类场，但在软材料和结构化材料的裂纹附近，载荷通过离散链、纤维或支柱传递，连续介质描述在此失效。本文针对含非线性链的晶格网络，构建了离散裂纹尖端理论，该理论包含两个核心部分：其一，大变形时，第i层代表性链的应变近似线性依赖于施加的宏观应变，即ε_i≈k_i(λ-1)，由此定义与层相关的应变放大因子k_i；其二，沿拓扑选定的链方向（称为离散HRR线），k_i的层间比值遵循双标度律。对于幂指数为p的幂律链力-应变关系，内部离散区域预测ε_i∝i^{-1/p}、f_i∝i^{-1}，这与经典连续介质HRR预测不同。该理论还解释了为何随网络尺寸增大，固有断裂能趋近于与尺寸无关的极限，光弹性水凝胶实验进一步验证了本文的理论。这些结果揭示了非线性晶格网络中双区域裂纹尖端标度律，为预测链变形与固有断裂能提供了框架。
英文摘要
Crack-tip fields govern deformation localization and failure initiation. Classical continuum fracture mechanics describes these fields through theories such as the Hutchinson-Rice-Rosengren (HRR) field for nonlinear power-law solids. However, continuum descriptions break down near cracks in soft and architected materials, where load is transmitted through discrete chains, fibers, or struts. Here, we develop a discrete crack-tip theory for lattice networks with nonlinear chains. The theory has two central components. First, at large deformation, the strain of a representative chain in layer $i$ depends approximately linearly on the applied macroscopic strain, $\varepsilon_i\approx k_i(λ-1)$, defining a layer-dependent strain-amplification factor $k_i$. Second, along topology-selected chain directions, termed discrete HRR lines, the layer-to-layer ratios of $k_i$ follow a two-regime scaling law. Together, for a power-law chain force-strain relation with exponent $p$, the inner discrete regime predicts $\varepsilon_i\sim i^{-1/p}$ and $f_i\sim i^{-1}$, which differs from the classical continuum HRR prediction. The theory also explains why the intrinsic fracture energy approaches a size-independent limit as the network size increases. Photoelastic hydrogel experiments further validate our theory. These results reveal a two-regime crack-tip scaling law in nonlinear lattice networks and provide a framework for predicting chain deformation and intrinsic fracture energy.
