Variable-order fracture mechanics and its application to dynamic fracture
Variable-order fracture mechanics and its application to dynamic fracture
复制标题
DOI：
10.1038/s41524-021-00492-x
复制
发表时间：
2021-02-05
影响因子：
9.7
通讯作者：
Semperlotti, Fabio
中科院分区：
文献类型：
--
作者：
Patnaik, Sansit;Semperlotti, Fabio
本研究提出了基于变阶力学概念的理论框架的公式、数值解和验证，该框架能够模拟脆性和准脆性固体的动态断裂。更具体地说，通过变量和分数阶算子重新表述弹性动力学问题，可以提供一种独特且极其强大的方法来模拟动态载荷下固体中裂纹的成核和扩展。由此产生的动态断裂公式是完全演化的，因此能够分析复杂的裂纹模式，而不需要对损伤位置和增长路径进行任何先验假设，并且不需要使用任何算法来数字跟踪演化的裂纹表面。变阶形式主义的演化性质也不需要额外的偏微分方程来预测损伤场的演化，因此表明复杂性和计算成本显着降低。值得注意的是，变阶公式自然能够捕获动态裂纹扩展的极其详细的特征，例如裂纹表面粗糙度以及单分支和多分支。通过将直接数值模拟的结果与文献中可用的典型基准问题的实验数据进行比较，验证了所提出的变阶公式的准确性和鲁棒性。
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.