基于扩展有限元法的混凝土细观断裂破坏过程模拟

扩展有限元法（XFEM）是分析不连续力学问题（特别是断裂问题）的一种有效的数值方法。在常规的有限元位移模式中，基于单位分解的思想加入一个跳跃函数和渐进缝尖位移场来对不连续体附近的节点自由度进行局部加强，从而反映了位移的不连续性。介绍了扩展有限元的基本原理，给出了扩展有限元进行混凝土开裂及裂纹扩展的分析方法，最后采用扩展有限元法模拟了湿筛混凝土单轴拉伸作用下及WinklerL-型混凝土板的细观断裂破坏过程。分析了混凝土裂纹萌生、扩展的过程及破坏形态，数值结果与实验结果吻合良好。研究表明：扩展有限元法通过特定的位移模式，使裂纹两侧不连续位移场的表达独立于网格划分，能有效地模拟混凝土材料细观断裂破坏过程。

Simulation of meso-fracture process of concrete using the extended finite element method

The XFEM(Extended Finite Element Method) is a new and effective simulation method for analyzing the discontinuity mechanical issues,especially the fracture problem.In the XFEM,in order to reflect the discontinuities of displacement,a jump function and asymptotic crack-tip displacement fields are added to the common finite element approximation for the local enrichment based on the framework of partition of unity.The basic theory of the XFEM is introduced firstly,and the method for analyzing the fracture and crack growth of meso concrete is presented.Finally,the meso fracture processes of wet-screened concrete specimens under uniaxial tension and Winkler L-shape concrete plate are investigated by the XFEM.The concrete crack initiations,the process of expansion and failure modes are given out in the study.The simulation results agree remarkably well with the experimental observations.The results indicate that the XFEM is an efficient method to simulate the fracture process of concrete materials because the expression of displacement discontinuities on both sides of crack is independent of element meshes.