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 引用本文: 王承强, 郑长良. 混凝土双K断裂参数计算的半解析有限元法[J]. 力学学报, 2004, 36(4): 414-418.
Semi-analytical element method for double-K fracture parameters computations in concrete[J]. Chinese Journal of Theoretical and Applied Mechanics, 2004, 36(4): 414-418.
 Citation: Semi-analytical element method for double-K fracture parameters computations in concrete[J]. Chinese Journal of Theoretical and Applied Mechanics, 2004, 36(4): 414-418.

## Semi-analytical element method for double-K fracture parameters computations in concrete

• 摘要: 混凝土裂缝扩展的双K断裂准则，用于描述混凝土结构裂缝的起裂、稳定扩展和失稳断裂. 其相应的双K断裂参数(起裂断裂韧度K_\rm IC^\rm ini 和失稳断裂韧度K_\rm IC^\rm un)一般通过简便的试验和基于虚拟裂缝扩展粘聚力的解析方法确定. 利用平面扇形域哈密顿体系的方程，通过分离变量法及共轭辛本征函数向量展开法，以解析的方法推导出基于混凝土虚拟裂缝扩展线性粘聚力模型的平面裂缝解析元列式. 将该解析元与有限元相结合，构成半解析的有限元法，可求解任意结构几何形状的混凝土平面裂缝双K断裂参数的计算问题.数值计算结果表明半解析有限元法对该类问题的求解是十分有效的.

Abstract: The double-K fracture criterion describes initiation,stable propagation and unstable propagation of cracks in concretestructures. The corresponding double-K fracture parameters (initialcracking roughness K_\rm IC^\rm ini and unstable fracture toughnessK_\rm IC^\rm un) introduced in the criterion are determined using asimple experiment method combing with an analytical evaluation based on thecohesive force on the fictitious crack zone. Based on the Hamiltoniangoverning equations of plane elasticity for sectorial domain, the variableseparation and eigenfunction expansion techniques are employed to develop anovel analytical finite element for the fictitious crack propagation linearforce model in fracture mechanics of concrete in this paper. The newanalytical element can be implemented into FEM program systems to solvecomputational problems of double-K fracture parameters for concrete crackedplane structures with arbitrary shapes. Numerical results indicate that themethod is efficient and accurate.

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