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

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.