Li Zhuheng
State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116024, China.
Materials (Basel). 2022 Feb 8;15(3):1251. doi: 10.3390/ma15031251.
Aiming at the numerical simulation of the entire crack propagation process in concrete, a numerical method is proposed, in which cohesive stress on the fracture process zone (FPZ) is simulated and applied by a nonlinear spring element. Using displacement control, the cohesive stress values on the FPZ are obtained from solving a system of nonlinear equations through an iterative process. According to a crack propagation criterion based on initial fracture toughness, the approach adds the spring elements to finite element analysis when simulating mode I crack propagation in standard three-point bending notched concrete beams with different strengths, initial crack ratios (a0/D), and depths (D). The simulated load versus displacement (P-Delta) curves are performed to recalculate the fracture energy and verify the accuracy of cohesion in the proposed method. The simulated load versus crack mouth opening displacement (P-CMOD) curves are consistent with the previous experimental results. Subsequently, the variations of the FPZ length and the crack extension resistance (KR) curves are studied according to the proposed iterative approach. Compared with the existing methods using a noniterative process, the iterative approach generates a larger maximum FPZ length and KR curve where the FPZ length is mainly determined by the fracture energy, tensile strength, and geometry shape of the beam, and the KR curve is primarily determined by the fracture energy and FPZ length. The significant differences in numerical results indicate that the applying cohesion is essential in numerical simulation. It is reasonable to conclude that the proposed nonlinear spring element is more applicable and practical in the numerical simulation of the concrete mode I crack propagation process by improving the accuracy of the cohesion applied on the FPZ.
针对混凝土中整个裂纹扩展过程的数值模拟，提出了一种数值方法，其中通过非线性弹簧单元模拟并应用断裂过程区（FPZ）上的粘结应力。采用位移控制，通过迭代过程求解非线性方程组来获得FPZ上的粘结应力值。根据基于初始断裂韧性的裂纹扩展准则，该方法在模拟不同强度、初始裂纹比（a0/D）和深度（D）的标准三点弯曲缺口混凝土梁中的I型裂纹扩展时，将弹簧单元添加到有限元分析中。通过模拟荷载-位移（P-Δ）曲线来重新计算断裂能，并验证所提方法中粘结力的准确性。模拟的荷载-裂纹开口位移（P-CMOD）曲线与先前的实验结果一致。随后，根据所提的迭代方法研究了FPZ长度和裂纹扩展阻力（KR）曲线的变化。与使用非迭代过程的现有方法相比，迭代方法产生的最大FPZ长度和KR曲线更大，其中FPZ长度主要由梁的断裂能、抗拉强度和几何形状决定，而KR曲线主要由断裂能和FPZ长度决定。数值结果的显著差异表明，在数值模拟中应用粘结力至关重要。可以合理地得出结论，通过提高施加在FPZ上的粘结力的精度，所提的非线性弹簧单元在混凝土I型裂纹扩展过程的数值模拟中更适用、更实用。
