AI 中文总结
本文研究弹性界面超越线性区域的稳定性，通过断裂力学模拟发现韧性异质性可诱导裂纹前缘失稳形成指状结构，揭示了与经典鞍结分岔不同的全局失稳机制，为理解异质固体的脆性-准脆性转变提供了新视角。
AI 中文摘要
我们通过研究盘状裂纹前缘在韧性异质介质中的扩展，来探究弹性界面超越线性区域的稳定性。利用断裂力学模拟，我们驱动裂纹前缘穿过具有可调韧性对比度的障碍物阵列。在低对比度下，裂纹前缘刚度保持有限，稳定了前缘扰动；然而，当对比度超过临界阈值时，刚度消失，前缘失稳为长指状，这些指状会发展为在障碍物之间扩展的子裂纹，而原始裂纹保持钉扎状态。在阈值附近，裂纹前缘响应呈现经典鞍结分岔的特征平方根标度行为，但我们的分析揭示了一种根本不同的机制：稳定的能量最小化裂纹前缘构型并未与不稳定对应物碰撞就消失了，相反，这种不稳定性源于沿裂纹前缘非局域相互作用所决定的与格里菲斯兼容的平衡态的全局丧失。除断裂力学外，这些发现指向非局域弹性界面中更广泛的一类集体全局分岔，可能有助于解释异质固体中从脆性到准脆性的转变。
英文摘要
We investigate the stability of elastic interfaces beyond the linear regime by considering penny-shaped crack fronts propagating through toughness heterogeneities. Using fracture mechanics simulations, we drive crack fronts through arrays of obstacles with tunable toughness contrast. At low contrast, the crack front stiffness remains finite and stabilizes front perturbations. Above a critical threshold, however, the stiffness vanishes and the front destabilizes into long fingers that evolve into daughter cracks propagating between obstacles while the original crack remains pinned. Near threshold, the crack front response displays the characteristic square-root scaling behavior of classical saddle-node bifurcations. Yet, our analysis reveals a fundamentally different mechanism: the stable energy-minimizing crack-front configuration disappears without colliding with an unstable counterpart. Instead, the instability originates from a global loss of Griffith-compatible equilibria governed by the nonlocal interactions along the crack front. Beyond fracture mechanics, these findings point toward a broader class of collective global bifurcations in nonlocal elastic interfaces and may help rationalize the brittle-to-quasibrittle transition in heterogeneous solids.
CommentsSubmitted to Physical Review Letters, 6 pages, 4 figures - main text, 5 pages, 5 figures - appendix
