准脆性材料中强不连续问题的数值方法若干应用及其研究进展

综述了模拟准脆性材料开裂过程的数值计算方法的研究进展和工程应用,比较了表征强不连续问题的显式非连续模型和隐式非连续模型的优缺点.结合混凝土粘结裂纹, 重点讨论了嵌入非连续模型,扩展有限元方法和富集有限元技术等非连续方法的构造特征和本质区别.从各种富集方法的理论完备性考察,以假定发展应变为基础的嵌入非连续方法虽然可以解决混凝土开裂过程中的应力锁死,满足内部边界的静力平衡条件以及反映开裂后的位移不连续问题,但嵌入非连续所采用的富集函数在开裂单元中并不能满足协调条件,使非连续两侧的应变不独立. 其局限性是由于富集自由度在单元的水平上引入,而以单位分解为基础的扩展有限元和富集有限元的富集函数以节点自由度的方式引入,除具有嵌入非连续的优点, 还可以有效消除嵌入非连续引起裂纹两侧应变的相互影响.文中同时指出了网格重构技术,弥散裂纹模型的局限性以及扩展有限元和富集有限元技术在构造方式上的细微差别.对于节点自由度方式引入的富集函数, 其操作困难性在文中也作了说明. 

SOME APPLICATIONS AND RECENT ADVANCES OF NUMERICAL METHODS FOR STRONG DISCONTINUITIES IN QUASI- BRITTLE MATERIAL

Research developments and engineering applications of numerical methods for simulating fracture process in quasi-brittle materials are reviewed and advantages and disadvantages of implicit and explicit representations of strong discontinuities such as crack are discussed. Focus is placed on their construction features and differences, concerning concrete cohesive cracks with emphasis on elements with embedded discontinuity model, on extended finite element method (XFEM) and on enriched finite element technique. From the viewpoint of completeness, the element with embedded discontinuity (EED) based on enhanced assumed strain can eliminate stress lock, enforce internal equilibrium conditions and reasonably represent a complete separation at late stages of the fracture process, but the enrichment functions applied in EED do not satisfy the compatibility conditions in the cracked element. The fact that the additional freedom introduced in the element level leads to a dependence of strain on both side of crack. Applying the additional freedom as a global freedom in XFEM, the enriched finite element based on the partition of unity not only has the advatages that EED has, but also can avoid the strain dependence on both side of crack. Certain limitations of remeshing and smeared crack model and the subtle difference between XFEM and the enriched finite element method are also pointed out.