:为解决传统内嵌裂缝模型仅能考虑定常位移跳跃而导致的应力闭锁问题,并保证裂缝张开位 移在相邻单元间的连续性,基于强不连续问题位移场的多尺度统一表述,选取具有明确物理意义的 裂缝节点(裂缝与单元边的交点)位移跳跃作为增强自由度,提出了适用于混凝土等准脆性材料和 结构破坏全过程分析的扩展内嵌裂缝模型,并给出了其有限元实现方法。 对楔入劈拉试验玉型和 单边缺口梁混合型破坏等混凝土标准试验进行了数值分析,得到的裂缝路径和荷载 位移曲线均与 试验结果或文献结果吻合良好,验证了模型理论的有效性,同时分析结果也表明该模型具有较高的 粗网格精度和良好的数值健壮性。 关键词:混凝土;损伤与破坏;内嵌裂缝模型;应力闭锁;有限元方法 中图分类号:TU311郾 4; O346郾 5 文献标志码:A 文章编号:1006 7647(2016)01 0053 07 Extended embedded crack finite element method for modeling localized failures in concrete structures/ / WU Jianying1, 2 , LI Fengbo1 , XU Shilang1(1. Department of Civil Engineering, Zhejiang University, Hangzhou 310058, China; 2. State Key Laboratory of Subtropic Building Science, South China University of Technology, Guangzhou 510641, China) Abstract: A novel extended embedded crack finite element method (XE鄄FEM) is proposed for modeling localized failures in concrete鄄like quasi鄄brittle materials and structures. Based on the unified multi鄄scale kinematics recently developed by the authors, the displacement jumps at the cracking nodes, where cracks intersect with the element edges, are selected as the elemental enrichment parameters. In addition to constant displacement jumps induced by relative translations of rigid bodies, linear deformation modes caused by rigid body rotation and self鄄stretching are consistently accounted for in the kinematics, so that the spurious stress locking can be removed. The enrichment parameters, which are shared by neighboring elements, can be regarded as global variables in the numerical implementation. Thus, the continuity of the displacement jumps can be guaranteed along the crack propagation path. Two benchmark tests of concrete structures, i. e. , the wedge鄄splitting test with mode鄄I failure and the single鄄edge notched beam with mixed鄄mode failure, were numerically simulated to validate the suggested method. The calculated response of load versus displacement and crack paths were compared to available experimental data and numerical results obtained from other methods. It is shown that the suggested method is stable and robust, with a high resolution in regard to coarse meshes. Key words: concrete; damage and failure; embedded crack model; stress locking; finite element method 混凝土在高层建筑、高速铁路、高速公路、水工 结构、桥梁涵隧等重大土木工程结构中应用十分广 泛。 作为典型的准脆性材料,混凝土裂缝的非线性 演化和扩展是导致结构完整性降低甚至发生破坏的 罪魁祸首,因此,保证混凝土结构安全服役必须全面 地掌握裂缝,并客观准确地反映裂缝非线性演化对材 料力学性能劣化和结构损伤破坏过程的影响规律。 内嵌 裂 缝 模 型 ( EFEM) 和 扩 展 有 限 元 方 法 (XFEM)是研究混凝土裂缝非线性演化的两类有效 途径,它们均可将裂缝嵌入到单元的任意位置,裂缝 处的本构行为一般采用基于混凝土断裂能的黏聚裂 缝模型加以描述,并通过裂缝跟踪算法保证计算结 果与有限元网格排列方向无关。 二者的区别在于, EFEM 在单元层次直接考虑裂缝引起的位移不连 续,并将裂缝处的牵引力连续条件作为求解附加未 知量的补充方程,而 XFEM 则采用普通节点的增强

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