npj: 动态断裂研究的福音—变阶力学新理论

断裂是横跨土木、机械和航空工程等广泛领域的结构系统中最常见的失效模式之一。防止断裂引起的破坏是结构设计的主要关注点，并且历史上一直在推动理论和实验方法的发展，以预测结构破坏的成核和传播。由于在多个空间尺度上同时存在多个物理过程，因此断裂力学的一般主题本身非常复杂，而动态裂纹的特定主题由于裂纹表面粗糙，不稳定性和分支而可能更具挑战性。在过去的几十年中，由于数值方法的迅速发展，动态裂缝的分析取得了重大进展。从动态建模角度看，可用于破坏分析的方法可以分为两类，即离散和连续。离散方法计算步骤非常繁杂，连续体方法的高计算成本都是制约动态破坏研究的重要因素。

来自美国普渡大学机械工程学院的Ray W. Herrick实验室的Sansit Patnaik教授等，通过可变和分数阶算子对弹性动力学问题进行了重新公式化，推导出一种独特且功能强大的方法来模拟在动态载荷下固体中裂缝的成核和扩展。其推导的最终动态裂缝公式是完全演化的，因此可以分析复杂的裂缝模式，而无需对损伤位置和生长路径进行任何先验假设，也无需使用任何算法来数值跟踪演化的裂缝表面。该方法避免了额外的偏微分方程来预测损伤场的演化，从而显著降低了复杂性和计算成本。通过三个基准实验，即1）Kalthoff-Winkler实验中涉及双缺口试样的冲击剪切载荷，（2）动态裂纹分支实验，（3）约翰-沙赫（John-Shah）实验的对比，验证了该理论计算框架的准确性与有效性。本研究提出的基于变阶力学的的理论框架，动态断裂的研究提供了强大的分析计算工具。

Variable-order fracture mechanics and its application to dynamic fracture

Sansit Patnaik & Fabio Semperlotti

This study presents the formulation, the numerical solution, and the validation of a theoretical framework based on the concept of variable-order mechanics and capable of modeling dynamic fracture in brittle and quasi-brittle solids. More specifically, the reformulation of the elastodynamic problem via variable and fractional-order operators enables a unique and extremely powerful approach to model nucleation and propagation of cracks in solids under dynamic loading. The resulting dynamic fracture formulation is fully evolutionary, hence enabling the analysis of complex crack patterns without requiring any a priori assumption on the damage location and the growth path, and without using any algorithm to numerically track the evolving crack surface. The evolutionary nature of the variable-order formalism also prevents the need for additional partial differential equations to predict the evolution of the damage field, hence suggesting a conspicuous reduction in complexity and computational cost. Remarkably, the variable-order formulation is naturally capable of capturing extremely detailed features characteristic of dynamic crack propagation such as crack surface roughening as well as single and multiple branching. The accuracy and robustness of the proposed variable-order formulation are validated by comparing the results of direct numerical simulations with experimental data of typical benchmark problems available in the literature.