SBFEM与非局部宏微观损伤模型相结合的准脆性材料开裂模拟

混凝土是一种被广泛应用于土木和水利工程中的准脆性材料, 在各种内外部因素的作用下, 开裂是混凝土结构最为普遍的破坏形式, 准确模拟结构的开裂过程, 对于结构的安全评估至关重要. 将比例边界有限元与非局部宏微观损伤模型相结合提出一种准脆性材料开裂模拟新方法. 以比例边界有限元子域的比例中心作为物质点, 通过两比例中心(物质点对)之间的物质键的正伸长率来定义微细观损伤, 将某点影响域内物质键的微细观损伤加权平均得到该点的宏观拓扑损伤. 再引入能量退化函数, 将宏观拓扑损伤嵌入到比例边界有限元的基本框架中. 充分利用比例边界有限元网格允许存在悬挂节点的优势, 采用四叉树网格离散技术进行快速、高质量的多级网格划分与过渡. 通过一个I型开裂与一个混合型开裂的两个典型算例, 验证了该方法可捕获结构裂纹扩展路径与荷载变形曲线. 与现有的方法相比, 本文的损伤模型可得到更准确的局部开裂损伤带, 结果更为合理, 且具有更高的计算精度和计算效率. 当损伤过程区网格尺寸小于影响域半径的1/5时, 计算结果不存在网格敏感性问题. 

CRACKING SIMULATION OF QUASI-BRITTLE MATERIALS BY COMBINING SBFEM WITH NONLOCAL MACRO-MICRO DAMAGE MODEL1)

Concrete is a typical quasi-brittle material which is widely used in civil engineering and hydraulic engineering. Under the influence of various internal and external factors, cracking is the most commonly encountered failure mode of concrete structure. It is of great importance to accurately simulate the cracking process of structures for the safety evaluation of concrete structures. A new crack initiation and propagation simulation method for quasi-brittle materials is proposed by combing scaled boundary finite element method and nonlocal macro-micro damage model. The scaling centre of the scaled boundary finite element subdomain is taken as the material point. The microscopic damage is defined in terms of the stretch rate of bonds of material points, and then the macro-scale topologic damage is evaluated as the weighted averaging of micro-scale damage over bonds in the influence domain. Through the energetic degradation function, which connects the energy-based damage and the macro-scale topologic damage, the nonlocal macro-micro damage model is inserted into the framework of scaled boundary finite element method. The quadtree mesh discrete technique is used to achieve fast and high-quality multilevel mesh by taking full advantage of the hanging nodes allowed in the scaled boundary finite element mesh. Two typical examples including a mode I and a mixed-mode cracking simulation show that the proposed method can be used to simulate crack initiation and propagation of quasi-brittle materials and capture the correct crack propagation path and load-deformation curve. Compared with other existing methods, using the nonlocal macro-micro damage model in this paper can obtain more accurate local cracking damage zone, and the results are more reasonable with higher calculation accuracy and efficiency. The numerical examples also indicate that there is no mesh sensitivity problem when the mesh size of the damage process region is less than 1/5 of the radius of the influence domain.