A novel multi-level model for quasi-brittle cracking analysis with complex microstructure

Abstract

The paper presents a novel multi-level model for quasi-brittle cracking analysis. Based on the partition of unity and information transmission technology, it provides a new non-re-meshing way to describe the cracking phenomenon in structures constructed from materials with complex microstructures. In the global model the concept of the material particle is defined and the basic unknowns are the boundary displacements of these particles, which is different from the concept of the traditional displacement field. A series of enrichment functions with continuous steps is proposed, describing the boundary displacement affected by crack bands and allowing the intersections of crack bands with particle boundaries a priori unknown. Simultaneously, additional equations are introduced to determine element status and make the degrees of freedom of the global model remain at a stable level. Compared with previous research by our group, where the local description is equal to the global description on the boundary of a material particle, the introduced enrichment functions enable more accurate capture of the characteristics of the crack band. The model avoids the complex and dynamic model adjustments due to the activation and exit of representative volume elements (RVEs) and the accuracy of the description of the crack pattern can be ensured. The RVEs are activated at first, but then many of them exit the computation due to the unloading which reduces many of the degrees of freedom. Two examples of concrete specimens are analyzed, and the concrete fracture experiment and the digital image correlation (DIC) test are conducted. Compared with the reference solutions and the experimental data, even though the microstructure of concrete is very complex, the cracking process and crack pattern can be obtained accurately.

概要

目的

建立完全无需进行网格重划分且能够有效提高裂纹带模拟精度的多层级模型。

创新点

1. 建立了材料粒子边界位移为基本未知量的全局控制方程,避免了全局层级材料粒子内部复杂状态的讨论;2. 将具有连续台阶的富集函数用于描述粒子边界的开裂位移,可以得到先验未知解;3. 建立了控制单元状态的补充方程,使全局模型的自由度数稳定在低水平;4. 实现了代表性体积元(RVE)的退出,进而将模型整体的自由度数控制在稳定的低水平;5. 裂纹带可以在任意位置进入和离开材料粒子。

方法

1. 采用多层级信息传递方法建立模型;2. 采用单位分解法的思想对材料粒子边界位移进行近似。

结论

1. 实现了计算过程中RVE的动态激活和退出,大大降低了整个模型的自由度数;2. 模型的模拟结果与完全微观模型及实验的结果一致,说明本文所提出的模型具有较高的计算精度。