考虑混凝土塑性耗散的CDM-XFEM裂缝计算方法

混凝土结构在服役期间受外界载荷的影响容易产生裂缝, 导致结构刚度降低、构件承载性能衰退, 而采用准确的计算方法预测混凝土裂缝的发展是治理裂缝的基本前提, 也是保障结构安全的重要手段. 连续损伤力学方法(continuou damage method, CDM)能够描述微裂缝的扩展过程, 但不能表示离散的开裂面, 且存在网格诱导偏差及虚假应力传递的弊端, 扩展有限单元法(mechanics-extended finite element method, XFEM)能够描述宏观裂纹的扩展过程, 但不能反映微裂缝的动态扩展, 两者计算出的裂纹分布与实际差异均较大. 现有的CDM-XFEM方法已经能够模拟混凝土微裂缝及宏观裂缝发展的整个过程, 但忽略了宏观裂缝出现时混凝土产生的塑性应变, CDM与XFEM的能量转化过程欠缺平衡性. 因此, 本文重点考虑能量转化时的塑性耗散, 选取指数型函数为粘结裂缝的牵引-分离模式, 基于能量及应力等效的条件重新构建了CDM与XFEM之间的能量转化方程. 采用广义逆最小二乘法求解能量转化系数, 确定能量转化时的临界位移, 并给出了裂缝面水平集的更新算法及整体计算方法的程序流程. 以双切口混凝土受剪拉开裂试验为例, 采用多种裂缝计算方法与试验进行了对比. 结果表明, 采用考虑混凝土塑性耗散的CDM-XFEM方法算出的裂缝分布及拉力-张开位移曲线与试验结果差异最小, 说明采用考虑混凝土塑性耗散的CDM-XFEM计算方法能够更好地计算混凝土裂缝. 

CDM-XFEM METHOD FOR CRACK CALCULATION CONSIDERED PLASTIC DISSIPATION OF CONCRETE

The concrete structure is easy to appear cracks under external loading during service, which leads to the reduction of structural stiffness and the decline of bearing capacity. Using accurate calculation method to predict the cracks development of concrete is the basic premise for crack control, and also the important measure to ensure the safety of structure. Continuous damage method (CDM) can describe the propagation process of micro cracks, but cannot represent discrete crack surface and contained disadvantages of grid induced deviation and false stress transfer, mechanics-extended finite element method (XFEM) can describe the propagation process of macro cracks, but cannot reflect the dynamic propagation of micro cracks, the cracks distribution calculated by the two methods are all quite different from the actual situation. The existing CDM-XFEM method can effectively simulate the whole process of concrete micro and macro cracks development, but the concrete plastic strain is ignored when the macro cracks appeared, so the energy conversion between CDM and XFEM is lack of balance. In this paper, the plastic dissipation of energy conversion is considered, the exponential function is selected as the traction separation mode of cohesive crack, based on the principle of energy and stress equivalence, the energy conversion equation between CDM and XFEM is reconstructed, the generalized inverse least square method is used to solve the energy conversion coefficient and determine the critical displacement during energy conversion, the updating algorithm of crack level set and overall calculation procedure are given out. Taking the shear tensile cracking experiment of concrete with double incisions as an example, various calculation methods of concrete crack are compared with the experiment. The results show that the crack distribution and tension-displacement curve calculated by CDM-XFEM method considered concrete plastic dissipation is most close to the experiment, which indicates that CDM-XFEM calculation method considered concrete plastic dissipation can better calculate concrete cracks.