The size effect of a quasi-brittle fracture is associated with the size of fracture process zone relative to the structural characteristic length. In numerical simulations using damage models, the nonlocal enhancement is commonly adopted to regularize the softening response. However, the conventional nonlocal enhancement, both integral and gradient approaches, induces a spurious spreading of damage zone. Since the evolution of fracture process zone cannot be captured well, the conventional nonlocal enhancement cannot predict the size effect phenomenon accurately. In this paper, the localizing gradient enhancement is adopted to avoid the spurious spreading of damage. Considering the three-point bend test of concrete beams, it is demonstrated that the dissipation profiles obtained with the localizing gradient enhancement compare well with those of reference meso-scale lattice models. With the correct damage evolution process, the localizing gradient enhancement is shown to capture the size effect phenomenon accurately for a series of geometrically similar concrete beams, using only a single set of material parameters.

准脆性断裂的尺寸效应与断裂过程区相对于结构特征长度的尺寸有关。在使用损伤模型的数值模拟中，通常采用非局部增强来规范化软化响应。但是，传统的非局部增强（积分和梯度方法）都会引起损伤区域的虚假扩展。由于不能很好地把握裂缝过程带的演化，因此传统的非局部增强方法无法准确预测尺寸效应现象。在本文中，采用局部梯度增强来避免损伤的虚假扩展。考虑到混凝土梁的三点弯曲试验，结果表明，通过局部梯度增强获得的耗散曲线与参考中尺度晶格模型的耗散曲线有很好的比较。通过正确的损伤演化过程，显示了局部梯度增强功能，仅使用一组材料参数即可精确捕获一系列几何相似的混凝土梁的尺寸效应现象。