Klein Yael, Sharon Eran
The Racah Institute of Physics, The Hebrew Univewrsity of Jerusalem, Jerusalem, 91904, Israel.
Phys Rev Lett. 2021 Sep 3;127(10):105501. doi: 10.1103/PhysRevLett.127.105501.
We present a unifying approach that describes both surface bending and fracture in the same geometrical framework. An immediate outcome of this view is a prediction for a new mechanical transition: the buckling-fracture transition. Using responsive gel strips that are subjected to nonuniform osmotic stress, we show the existence of the transition: Thin plates do not fracture. Instead, they release energy via buckling, even at strains that can be orders of magnitude larger than the Griffith fracture criterion. The analysis of the system reveals the dependence of the transition on system's parameters and agrees well with experimental results. Finally, we suggest a new description of a mode I crack as a line distribution of Gaussian curvature. It is thus exchangeable with extrinsic generation of curvature via buckling. The work opens the way for the study of mechanical problems within a single nonlinear framework. It suggests that fracture driven by internal stresses can be completely avoided by a proper geometrical design.
我们提出了一种统一的方法，该方法在相同的几何框架中描述了表面弯曲和断裂。这一观点的直接结果是对一种新的力学转变的预测：屈曲-断裂转变。通过使用承受非均匀渗透应力的响应性凝胶条，我们证明了这种转变的存在：薄板不会断裂。相反，即使在应变比格里菲斯断裂准则大几个数量级的情况下，它们也会通过屈曲来释放能量。对该系统的分析揭示了这种转变对系统参数的依赖性，并且与实验结果非常吻合。最后，我们提出了一种对I型裂纹的新描述，即高斯曲率的线分布。因此，它可与通过屈曲产生的外在曲率相互转换。这项工作为在单一非线性框架内研究力学问题开辟了道路。它表明，通过适当的几何设计可以完全避免由内应力驱动的断裂。
