基于扩展有限元法的混凝土三点弯曲梁裂缝扩展模拟研究

扩展有限元法(X-FEM)是一种研究裂纹扩展的有效路径,其基于单元分解的思想引入了加强函数,避免了在处理非连续问题时对网格重新划分。利用扩展有限元法模拟了混凝土三点弯曲梁开裂的全过程,得到了三点弯曲梁在不同缝高比、不同试件厚度条件下的荷载-位移曲线(P-CMOD),结合线性叠加原理和双K断裂准则计算其断裂参数,同时对这些参数进行比较分析。对不同距离偏置裂缝三点弯曲梁进行数值模拟,分析了初始裂缝位置对裂纹发展规律和承载力的影响。通过与已有试验得到的断裂规律进行比较,结果表明:起裂荷载和失稳荷载随缝高比增大而减小;随着试件厚度增大,起裂荷载和失稳荷载随之增大,但起裂韧度和失稳韧度没有明显变化;数值模拟结果符合试验的断裂规律,验证了扩展有限元的合理性。

Study on X-FEM-based simulation on crack-propagation of three-point bending concrete beam

The full-cracking process of three-point bending concrete beam is simulated with the extended finite element method (X － FEM)，and then the load-displacement curves (P － CMOD) of the beam under the conditions of different crack-height ratios，different specimen thicknesses are obtained. Combined with both the principle of linear superposition and the double-K fracture criterion，the fracturing parameters are calculated，while these parameters are comparatively analyzed at the same time as well. Numerical simulations are made on the three-point bending concrete beams with different distance-offset cracks，and then the influences from cracking development law and bearing capacity on the initial cracking locations are analyzed. Through the comparing with the fracturing law obtained from the existing experiment concerned，the results show that the cracking load and the instability load decrease with the increase of the crack-depth ratio. The cracking load and the instability load increase with the increase of the thickness of the samples，but there is no obvious change in the crack toughness and the instatility toughness. Its fracturing law that accords with the experiment is found out，thus the reasonability of the extended finite element method (X － FEM) is verified.