基于黏聚裂纹模型的混凝土断裂过程扩展有限元法模拟

为了解决混凝土材料的断裂问题,采用扩展有限元法结合黏聚裂纹模型对混凝土非线性断裂力学行为进行模拟。在黏聚裂纹模型中,裂纹附近应力场没有奇异性,因此,基于四结点四边形单元构造了一种新的黏聚裂纹模拟的扩展有限元位移模式,并采用符号函数对所有的开裂单元(包括裂纹贯穿单元和裂尖单元)进行加强。采用类似于"弧长法"的方案求解非线性控制方程。结果表明:该加强策略解决了裂尖单元裂纹两边应力不等的问题,其裂尖位置任意,且混合单元处理方便。通过数值模拟混凝土Ⅰ型和混合型断裂问题,将模拟结果与参考解及试验结果进行比较,误差均在5%以内,验证了该方法的可靠性。该方法采用统一的符号函数进行加强,编程更为方便。

Simulation of crack growth process in concrete using extended finite element method based on cohesive crack model

In order to solve the fracture problem of concrete materials， the extended finite element method combined with the cohesive crack model is used to simulate the nonlinear fracture mechanics behavior of concrete. In the cohesive crack model， there is no singularity in the stress field near the crack，based on the four-node quadrilateral element，a new extended finite element displacement model for cohesive crack modeling is developed. All cracked elements including the elements cut by crack and the tip element are enriched by the sign function. The reinforcement strategy solves the problem of unequal stress on both sides of the crack tip element and the crack tip position is arbitrary，and the mixing elements are easy to handle. The nonlinear governing equations are solved with a similar arc length method. Mode I and mixed-mode fracture problems in concrete are numerically simulated，and the reliability of the method is verified by comparing with the reference solutions and the experimental results. It is easy to develop code because the unified sign function is used as enrichment functions.